# Set minimal log verbosity
setVerbosity(MinimalLog)

# %% Si_long

# Set up lattice
vector_a = [19.200070429558327, 0.0, 0.0]*Angstrom
vector_b = [0.0, 19.200070429558327, 0.0]*Angstrom
vector_c = [0.0, 0.0, 129.4731]*Angstrom
lattice = UnitCell(vector_a, vector_b, vector_c)

# Define elements
elements = [Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon, Silicon, Silicon, Silicon,
            Silicon, Silicon, Silicon, Silicon]

# Define coordinates
fractional_coordinates = [[ 0.1           ,  0.            ,  0.010485961949],
                          [ 0.3           ,  0.            ,  0.010485961949],
                          [ 0.5           ,  0.            ,  0.010485961949],
                          [ 0.7           ,  0.            ,  0.010485961949],
                          [ 0.9           ,  0.            ,  0.010485961949],
                          [ 0.1           ,  0.2           ,  0.010485961949],
                          [ 0.3           ,  0.2           ,  0.010485961949],
                          [ 0.5           ,  0.2           ,  0.010485961949],
                          [ 0.7           ,  0.2           ,  0.010485961949],
                          [ 0.9           ,  0.2           ,  0.010485961949],
                          [ 0.1           ,  0.4           ,  0.010485961949],
                          [ 0.3           ,  0.4           ,  0.010485961949],
                          [ 0.5           ,  0.4           ,  0.010485961949],
                          [ 0.7           ,  0.4           ,  0.010485961949],
                          [ 0.9           ,  0.4           ,  0.010485961949],
                          [ 0.1           ,  0.6           ,  0.010485961949],
                          [ 0.3           ,  0.6           ,  0.010485961949],
                          [ 0.5           ,  0.6           ,  0.010485961949],
                          [ 0.7           ,  0.6           ,  0.010485961949],
                          [ 0.9           ,  0.6           ,  0.010485961949],
                          [ 0.1           ,  0.8           ,  0.010485961949],
                          [ 0.3           ,  0.8           ,  0.010485961949],
                          [ 0.5           ,  0.8           ,  0.010485961949],
                          [ 0.7           ,  0.8           ,  0.010485961949],
                          [ 0.9           ,  0.8           ,  0.010485961949],
                          [ 0.1           ,  0.1           ,  0.020971923898],
                          [ 0.3           ,  0.1           ,  0.020971923898],
                          [ 0.5           ,  0.1           ,  0.020971923898],
                          [ 0.7           ,  0.1           ,  0.020971923898],
                          [ 0.9           ,  0.1           ,  0.020971923898],
                          [ 0.1           ,  0.3           ,  0.020971923898],
                          [ 0.3           ,  0.3           ,  0.020971923898],
                          [ 0.5           ,  0.3           ,  0.020971923898],
                          [ 0.7           ,  0.3           ,  0.020971923898],
                          [ 0.9           ,  0.3           ,  0.020971923898],
                          [ 0.1           ,  0.5           ,  0.020971923898],
                          [ 0.3           ,  0.5           ,  0.020971923898],
                          [ 0.5           ,  0.5           ,  0.020971923898],
                          [ 0.7           ,  0.5           ,  0.020971923898],
                          [ 0.9           ,  0.5           ,  0.020971923898],
                          [ 0.1           ,  0.7           ,  0.020971923898],
                          [ 0.3           ,  0.7           ,  0.020971923898],
                          [ 0.5           ,  0.7           ,  0.020971923898],
                          [ 0.7           ,  0.7           ,  0.020971923898],
                          [ 0.9           ,  0.7           ,  0.020971923898],
                          [ 0.1           ,  0.9           ,  0.020971923898],
                          [ 0.3           ,  0.9           ,  0.020971923898],
                          [ 0.5           ,  0.9           ,  0.020971923898],
                          [ 0.7           ,  0.9           ,  0.020971923898],
                          [ 0.9           ,  0.9           ,  0.020971923898],
                          [ 0.            ,  0.1           ,  0.031457885847],
                          [ 0.2           ,  0.1           ,  0.031457885847],
                          [ 0.4           ,  0.1           ,  0.031457885847],
                          [ 0.6           ,  0.1           ,  0.031457885847],
                          [ 0.8           ,  0.1           ,  0.031457885847],
                          [ 0.            ,  0.3           ,  0.031457885847],
                          [ 0.2           ,  0.3           ,  0.031457885847],
                          [ 0.4           ,  0.3           ,  0.031457885847],
                          [ 0.6           ,  0.3           ,  0.031457885847],
                          [ 0.8           ,  0.3           ,  0.031457885847],
                          [ 0.            ,  0.5           ,  0.031457885847],
                          [ 0.2           ,  0.5           ,  0.031457885847],
                          [ 0.4           ,  0.5           ,  0.031457885847],
                          [ 0.6           ,  0.5           ,  0.031457885847],
                          [ 0.8           ,  0.5           ,  0.031457885847],
                          [ 0.            ,  0.7           ,  0.031457885847],
                          [ 0.2           ,  0.7           ,  0.031457885847],
                          [ 0.4           ,  0.7           ,  0.031457885847],
                          [ 0.6           ,  0.7           ,  0.031457885847],
                          [ 0.8           ,  0.7           ,  0.031457885847],
                          [ 0.            ,  0.9           ,  0.031457885847],
                          [ 0.2           ,  0.9           ,  0.031457885847],
                          [ 0.4           ,  0.9           ,  0.031457885847],
                          [ 0.6           ,  0.9           ,  0.031457885847],
                          [ 0.8           ,  0.9           ,  0.031457885847],
                          [ 0.            ,  0.            ,  0.041943847796],
                          [ 0.2           ,  0.            ,  0.041943847796],
                          [ 0.4           ,  0.            ,  0.041943847796],
                          [ 0.6           ,  0.            ,  0.041943847796],
                          [ 0.8           ,  0.            ,  0.041943847796],
                          [ 0.            ,  0.2           ,  0.041943847796],
                          [ 0.2           ,  0.2           ,  0.041943847796],
                          [ 0.4           ,  0.2           ,  0.041943847796],
                          [ 0.6           ,  0.2           ,  0.041943847796],
                          [ 0.8           ,  0.2           ,  0.041943847796],
                          [ 0.            ,  0.4           ,  0.041943847796],
                          [ 0.2           ,  0.4           ,  0.041943847796],
                          [ 0.4           ,  0.4           ,  0.041943847796],
                          [ 0.6           ,  0.4           ,  0.041943847796],
                          [ 0.8           ,  0.4           ,  0.041943847796],
                          [ 0.            ,  0.6           ,  0.041943847796],
                          [ 0.2           ,  0.6           ,  0.041943847796],
                          [ 0.4           ,  0.6           ,  0.041943847796],
                          [ 0.6           ,  0.6           ,  0.041943847796],
                          [ 0.8           ,  0.6           ,  0.041943847796],
                          [ 0.            ,  0.8           ,  0.041943847796],
                          [ 0.2           ,  0.8           ,  0.041943847796],
                          [ 0.4           ,  0.8           ,  0.041943847796],
                          [ 0.6           ,  0.8           ,  0.041943847796],
                          [ 0.8           ,  0.8           ,  0.041943847796],
                          [ 0.1           ,  0.            ,  0.052429809745],
                          [ 0.3           ,  0.            ,  0.052429809745],
                          [ 0.5           ,  0.            ,  0.052429809745],
                          [ 0.7           ,  0.            ,  0.052429809745],
                          [ 0.9           ,  0.            ,  0.052429809745],
                          [ 0.1           ,  0.2           ,  0.052429809745],
                          [ 0.3           ,  0.2           ,  0.052429809745],
                          [ 0.5           ,  0.2           ,  0.052429809745],
                          [ 0.7           ,  0.2           ,  0.052429809745],
                          [ 0.9           ,  0.2           ,  0.052429809745],
                          [ 0.1           ,  0.4           ,  0.052429809745],
                          [ 0.3           ,  0.4           ,  0.052429809745],
                          [ 0.5           ,  0.4           ,  0.052429809745],
                          [ 0.7           ,  0.4           ,  0.052429809745],
                          [ 0.9           ,  0.4           ,  0.052429809745],
                          [ 0.1           ,  0.6           ,  0.052429809745],
                          [ 0.3           ,  0.6           ,  0.052429809745],
                          [ 0.5           ,  0.6           ,  0.052429809745],
                          [ 0.7           ,  0.6           ,  0.052429809745],
                          [ 0.9           ,  0.6           ,  0.052429809745],
                          [ 0.1           ,  0.8           ,  0.052429809745],
                          [ 0.3           ,  0.8           ,  0.052429809745],
                          [ 0.5           ,  0.8           ,  0.052429809745],
                          [ 0.7           ,  0.8           ,  0.052429809745],
                          [ 0.9           ,  0.8           ,  0.052429809745],
                          [ 0.1           ,  0.1           ,  0.062915771694],
                          [ 0.3           ,  0.1           ,  0.062915771694],
                          [ 0.5           ,  0.1           ,  0.062915771694],
                          [ 0.7           ,  0.1           ,  0.062915771694],
                          [ 0.9           ,  0.1           ,  0.062915771694],
                          [ 0.1           ,  0.3           ,  0.062915771694],
                          [ 0.3           ,  0.3           ,  0.062915771694],
                          [ 0.5           ,  0.3           ,  0.062915771694],
                          [ 0.7           ,  0.3           ,  0.062915771694],
                          [ 0.9           ,  0.3           ,  0.062915771694],
                          [ 0.1           ,  0.5           ,  0.062915771694],
                          [ 0.3           ,  0.5           ,  0.062915771694],
                          [ 0.5           ,  0.5           ,  0.062915771694],
                          [ 0.7           ,  0.5           ,  0.062915771694],
                          [ 0.9           ,  0.5           ,  0.062915771694],
                          [ 0.1           ,  0.7           ,  0.062915771694],
                          [ 0.3           ,  0.7           ,  0.062915771694],
                          [ 0.5           ,  0.7           ,  0.062915771694],
                          [ 0.7           ,  0.7           ,  0.062915771694],
                          [ 0.9           ,  0.7           ,  0.062915771694],
                          [ 0.1           ,  0.9           ,  0.062915771694],
                          [ 0.3           ,  0.9           ,  0.062915771694],
                          [ 0.5           ,  0.9           ,  0.062915771694],
                          [ 0.7           ,  0.9           ,  0.062915771694],
                          [ 0.9           ,  0.9           ,  0.062915771694],
                          [ 0.            ,  0.1           ,  0.073401733642],
                          [ 0.2           ,  0.1           ,  0.073401733642],
                          [ 0.4           ,  0.1           ,  0.073401733642],
                          [ 0.6           ,  0.1           ,  0.073401733642],
                          [ 0.8           ,  0.1           ,  0.073401733642],
                          [ 0.            ,  0.3           ,  0.073401733642],
                          [ 0.2           ,  0.3           ,  0.073401733642],
                          [ 0.4           ,  0.3           ,  0.073401733642],
                          [ 0.6           ,  0.3           ,  0.073401733642],
                          [ 0.8           ,  0.3           ,  0.073401733642],
                          [ 0.            ,  0.5           ,  0.073401733642],
                          [ 0.2           ,  0.5           ,  0.073401733642],
                          [ 0.4           ,  0.5           ,  0.073401733642],
                          [ 0.6           ,  0.5           ,  0.073401733642],
                          [ 0.8           ,  0.5           ,  0.073401733642],
                          [ 0.            ,  0.7           ,  0.073401733642],
                          [ 0.2           ,  0.7           ,  0.073401733642],
                          [ 0.4           ,  0.7           ,  0.073401733642],
                          [ 0.6           ,  0.7           ,  0.073401733642],
                          [ 0.8           ,  0.7           ,  0.073401733642],
                          [ 0.            ,  0.9           ,  0.073401733642],
                          [ 0.2           ,  0.9           ,  0.073401733642],
                          [ 0.4           ,  0.9           ,  0.073401733642],
                          [ 0.6           ,  0.9           ,  0.073401733642],
                          [ 0.8           ,  0.9           ,  0.073401733642],
                          [ 0.            ,  0.            ,  0.083887695591],
                          [ 0.2           ,  0.            ,  0.083887695591],
                          [ 0.4           ,  0.            ,  0.083887695591],
                          [ 0.6           ,  0.            ,  0.083887695591],
                          [ 0.8           ,  0.            ,  0.083887695591],
                          [ 0.            ,  0.2           ,  0.083887695591],
                          [ 0.2           ,  0.2           ,  0.083887695591],
                          [ 0.4           ,  0.2           ,  0.083887695591],
                          [ 0.6           ,  0.2           ,  0.083887695591],
                          [ 0.8           ,  0.2           ,  0.083887695591],
                          [ 0.            ,  0.4           ,  0.083887695591],
                          [ 0.2           ,  0.4           ,  0.083887695591],
                          [ 0.4           ,  0.4           ,  0.083887695591],
                          [ 0.6           ,  0.4           ,  0.083887695591],
                          [ 0.8           ,  0.4           ,  0.083887695591],
                          [ 0.            ,  0.6           ,  0.083887695591],
                          [ 0.2           ,  0.6           ,  0.083887695591],
                          [ 0.4           ,  0.6           ,  0.083887695591],
                          [ 0.6           ,  0.6           ,  0.083887695591],
                          [ 0.8           ,  0.6           ,  0.083887695591],
                          [ 0.            ,  0.8           ,  0.083887695591],
                          [ 0.2           ,  0.8           ,  0.083887695591],
                          [ 0.4           ,  0.8           ,  0.083887695591],
                          [ 0.6           ,  0.8           ,  0.083887695591],
                          [ 0.8           ,  0.8           ,  0.083887695591],
                          [ 0.1           ,  0.            ,  0.09437365754 ],
                          [ 0.3           ,  0.            ,  0.09437365754 ],
                          [ 0.5           ,  0.            ,  0.09437365754 ],
                          [ 0.7           ,  0.            ,  0.09437365754 ],
                          [ 0.9           ,  0.            ,  0.09437365754 ],
                          [ 0.1           ,  0.2           ,  0.09437365754 ],
                          [ 0.3           ,  0.2           ,  0.09437365754 ],
                          [ 0.5           ,  0.2           ,  0.09437365754 ],
                          [ 0.7           ,  0.2           ,  0.09437365754 ],
                          [ 0.9           ,  0.2           ,  0.09437365754 ],
                          [ 0.1           ,  0.4           ,  0.09437365754 ],
                          [ 0.3           ,  0.4           ,  0.09437365754 ],
                          [ 0.5           ,  0.4           ,  0.09437365754 ],
                          [ 0.7           ,  0.4           ,  0.09437365754 ],
                          [ 0.9           ,  0.4           ,  0.09437365754 ],
                          [ 0.1           ,  0.6           ,  0.09437365754 ],
                          [ 0.3           ,  0.6           ,  0.09437365754 ],
                          [ 0.5           ,  0.6           ,  0.09437365754 ],
                          [ 0.7           ,  0.6           ,  0.09437365754 ],
                          [ 0.9           ,  0.6           ,  0.09437365754 ],
                          [ 0.1           ,  0.8           ,  0.09437365754 ],
                          [ 0.3           ,  0.8           ,  0.09437365754 ],
                          [ 0.5           ,  0.8           ,  0.09437365754 ],
                          [ 0.7           ,  0.8           ,  0.09437365754 ],
                          [ 0.9           ,  0.8           ,  0.09437365754 ],
                          [ 0.1           ,  0.1           ,  0.104859619489],
                          [ 0.3           ,  0.1           ,  0.104859619489],
                          [ 0.5           ,  0.1           ,  0.104859619489],
                          [ 0.7           ,  0.1           ,  0.104859619489],
                          [ 0.9           ,  0.1           ,  0.104859619489],
                          [ 0.1           ,  0.3           ,  0.104859619489],
                          [ 0.3           ,  0.3           ,  0.104859619489],
                          [ 0.5           ,  0.3           ,  0.104859619489],
                          [ 0.7           ,  0.3           ,  0.104859619489],
                          [ 0.9           ,  0.3           ,  0.104859619489],
                          [ 0.1           ,  0.5           ,  0.104859619489],
                          [ 0.3           ,  0.5           ,  0.104859619489],
                          [ 0.5           ,  0.5           ,  0.104859619489],
                          [ 0.7           ,  0.5           ,  0.104859619489],
                          [ 0.9           ,  0.5           ,  0.104859619489],
                          [ 0.1           ,  0.7           ,  0.104859619489],
                          [ 0.3           ,  0.7           ,  0.104859619489],
                          [ 0.5           ,  0.7           ,  0.104859619489],
                          [ 0.7           ,  0.7           ,  0.104859619489],
                          [ 0.9           ,  0.7           ,  0.104859619489],
                          [ 0.1           ,  0.9           ,  0.104859619489],
                          [ 0.3           ,  0.9           ,  0.104859619489],
                          [ 0.5           ,  0.9           ,  0.104859619489],
                          [ 0.7           ,  0.9           ,  0.104859619489],
                          [ 0.9           ,  0.9           ,  0.104859619489],
                          [ 0.            ,  0.1           ,  0.115345581438],
                          [ 0.2           ,  0.1           ,  0.115345581438],
                          [ 0.4           ,  0.1           ,  0.115345581438],
                          [ 0.6           ,  0.1           ,  0.115345581438],
                          [ 0.8           ,  0.1           ,  0.115345581438],
                          [ 0.            ,  0.3           ,  0.115345581438],
                          [ 0.2           ,  0.3           ,  0.115345581438],
                          [ 0.4           ,  0.3           ,  0.115345581438],
                          [ 0.6           ,  0.3           ,  0.115345581438],
                          [ 0.8           ,  0.3           ,  0.115345581438],
                          [ 0.            ,  0.5           ,  0.115345581438],
                          [ 0.2           ,  0.5           ,  0.115345581438],
                          [ 0.4           ,  0.5           ,  0.115345581438],
                          [ 0.6           ,  0.5           ,  0.115345581438],
                          [ 0.8           ,  0.5           ,  0.115345581438],
                          [ 0.            ,  0.7           ,  0.115345581438],
                          [ 0.2           ,  0.7           ,  0.115345581438],
                          [ 0.4           ,  0.7           ,  0.115345581438],
                          [ 0.6           ,  0.7           ,  0.115345581438],
                          [ 0.8           ,  0.7           ,  0.115345581438],
                          [ 0.            ,  0.9           ,  0.115345581438],
                          [ 0.2           ,  0.9           ,  0.115345581438],
                          [ 0.4           ,  0.9           ,  0.115345581438],
                          [ 0.6           ,  0.9           ,  0.115345581438],
                          [ 0.8           ,  0.9           ,  0.115345581438],
                          [ 0.            ,  0.            ,  0.125831543387],
                          [ 0.2           ,  0.            ,  0.125831543387],
                          [ 0.4           ,  0.            ,  0.125831543387],
                          [ 0.6           ,  0.            ,  0.125831543387],
                          [ 0.8           ,  0.            ,  0.125831543387],
                          [ 0.            ,  0.2           ,  0.125831543387],
                          [ 0.2           ,  0.2           ,  0.125831543387],
                          [ 0.4           ,  0.2           ,  0.125831543387],
                          [ 0.6           ,  0.2           ,  0.125831543387],
                          [ 0.8           ,  0.2           ,  0.125831543387],
                          [ 0.            ,  0.4           ,  0.125831543387],
                          [ 0.2           ,  0.4           ,  0.125831543387],
                          [ 0.4           ,  0.4           ,  0.125831543387],
                          [ 0.6           ,  0.4           ,  0.125831543387],
                          [ 0.8           ,  0.4           ,  0.125831543387],
                          [ 0.            ,  0.6           ,  0.125831543387],
                          [ 0.2           ,  0.6           ,  0.125831543387],
                          [ 0.4           ,  0.6           ,  0.125831543387],
                          [ 0.6           ,  0.6           ,  0.125831543387],
                          [ 0.8           ,  0.6           ,  0.125831543387],
                          [ 0.            ,  0.8           ,  0.125831543387],
                          [ 0.2           ,  0.8           ,  0.125831543387],
                          [ 0.4           ,  0.8           ,  0.125831543387],
                          [ 0.6           ,  0.8           ,  0.125831543387],
                          [ 0.8           ,  0.8           ,  0.125831543387],
                          [ 0.1           ,  0.            ,  0.136317505336],
                          [ 0.3           ,  0.            ,  0.136317505336],
                          [ 0.5           ,  0.            ,  0.136317505336],
                          [ 0.7           ,  0.            ,  0.136317505336],
                          [ 0.9           ,  0.            ,  0.136317505336],
                          [ 0.1           ,  0.2           ,  0.136317505336],
                          [ 0.3           ,  0.2           ,  0.136317505336],
                          [ 0.5           ,  0.2           ,  0.136317505336],
                          [ 0.7           ,  0.2           ,  0.136317505336],
                          [ 0.9           ,  0.2           ,  0.136317505336],
                          [ 0.1           ,  0.4           ,  0.136317505336],
                          [ 0.3           ,  0.4           ,  0.136317505336],
                          [ 0.5           ,  0.4           ,  0.136317505336],
                          [ 0.7           ,  0.4           ,  0.136317505336],
                          [ 0.9           ,  0.4           ,  0.136317505336],
                          [ 0.1           ,  0.6           ,  0.136317505336],
                          [ 0.3           ,  0.6           ,  0.136317505336],
                          [ 0.5           ,  0.6           ,  0.136317505336],
                          [ 0.7           ,  0.6           ,  0.136317505336],
                          [ 0.9           ,  0.6           ,  0.136317505336],
                          [ 0.1           ,  0.8           ,  0.136317505336],
                          [ 0.3           ,  0.8           ,  0.136317505336],
                          [ 0.5           ,  0.8           ,  0.136317505336],
                          [ 0.7           ,  0.8           ,  0.136317505336],
                          [ 0.9           ,  0.8           ,  0.136317505336],
                          [ 0.1           ,  0.1           ,  0.146803467284],
                          [ 0.3           ,  0.1           ,  0.146803467284],
                          [ 0.5           ,  0.1           ,  0.146803467284],
                          [ 0.7           ,  0.1           ,  0.146803467284],
                          [ 0.9           ,  0.1           ,  0.146803467284],
                          [ 0.1           ,  0.3           ,  0.146803467284],
                          [ 0.3           ,  0.3           ,  0.146803467284],
                          [ 0.5           ,  0.3           ,  0.146803467284],
                          [ 0.7           ,  0.3           ,  0.146803467284],
                          [ 0.9           ,  0.3           ,  0.146803467284],
                          [ 0.1           ,  0.5           ,  0.146803467284],
                          [ 0.3           ,  0.5           ,  0.146803467284],
                          [ 0.5           ,  0.5           ,  0.146803467284],
                          [ 0.7           ,  0.5           ,  0.146803467284],
                          [ 0.9           ,  0.5           ,  0.146803467284],
                          [ 0.1           ,  0.7           ,  0.146803467284],
                          [ 0.3           ,  0.7           ,  0.146803467284],
                          [ 0.5           ,  0.7           ,  0.146803467284],
                          [ 0.7           ,  0.7           ,  0.146803467284],
                          [ 0.9           ,  0.7           ,  0.146803467284],
                          [ 0.1           ,  0.9           ,  0.146803467284],
                          [ 0.3           ,  0.9           ,  0.146803467284],
                          [ 0.5           ,  0.9           ,  0.146803467284],
                          [ 0.7           ,  0.9           ,  0.146803467284],
                          [ 0.9           ,  0.9           ,  0.146803467284],
                          [ 0.            ,  0.1           ,  0.157289429233],
                          [ 0.2           ,  0.1           ,  0.157289429233],
                          [ 0.4           ,  0.1           ,  0.157289429233],
                          [ 0.6           ,  0.1           ,  0.157289429233],
                          [ 0.8           ,  0.1           ,  0.157289429233],
                          [ 0.            ,  0.3           ,  0.157289429233],
                          [ 0.2           ,  0.3           ,  0.157289429233],
                          [ 0.4           ,  0.3           ,  0.157289429233],
                          [ 0.6           ,  0.3           ,  0.157289429233],
                          [ 0.8           ,  0.3           ,  0.157289429233],
                          [ 0.            ,  0.5           ,  0.157289429233],
                          [ 0.2           ,  0.5           ,  0.157289429233],
                          [ 0.4           ,  0.5           ,  0.157289429233],
                          [ 0.6           ,  0.5           ,  0.157289429233],
                          [ 0.8           ,  0.5           ,  0.157289429233],
                          [ 0.            ,  0.7           ,  0.157289429233],
                          [ 0.2           ,  0.7           ,  0.157289429233],
                          [ 0.4           ,  0.7           ,  0.157289429233],
                          [ 0.6           ,  0.7           ,  0.157289429233],
                          [ 0.8           ,  0.7           ,  0.157289429233],
                          [ 0.            ,  0.9           ,  0.157289429233],
                          [ 0.2           ,  0.9           ,  0.157289429233],
                          [ 0.4           ,  0.9           ,  0.157289429233],
                          [ 0.6           ,  0.9           ,  0.157289429233],
                          [ 0.8           ,  0.9           ,  0.157289429233],
                          [ 0.            ,  0.            ,  0.167775391182],
                          [ 0.2           ,  0.            ,  0.167775391182],
                          [ 0.4           ,  0.            ,  0.167775391182],
                          [ 0.6           ,  0.            ,  0.167775391182],
                          [ 0.8           ,  0.            ,  0.167775391182],
                          [ 0.            ,  0.2           ,  0.167775391182],
                          [ 0.2           ,  0.2           ,  0.167775391182],
                          [ 0.4           ,  0.2           ,  0.167775391182],
                          [ 0.6           ,  0.2           ,  0.167775391182],
                          [ 0.8           ,  0.2           ,  0.167775391182],
                          [ 0.            ,  0.4           ,  0.167775391182],
                          [ 0.2           ,  0.4           ,  0.167775391182],
                          [ 0.4           ,  0.4           ,  0.167775391182],
                          [ 0.6           ,  0.4           ,  0.167775391182],
                          [ 0.8           ,  0.4           ,  0.167775391182],
                          [ 0.            ,  0.6           ,  0.167775391182],
                          [ 0.2           ,  0.6           ,  0.167775391182],
                          [ 0.4           ,  0.6           ,  0.167775391182],
                          [ 0.6           ,  0.6           ,  0.167775391182],
                          [ 0.8           ,  0.6           ,  0.167775391182],
                          [ 0.            ,  0.8           ,  0.167775391182],
                          [ 0.2           ,  0.8           ,  0.167775391182],
                          [ 0.4           ,  0.8           ,  0.167775391182],
                          [ 0.6           ,  0.8           ,  0.167775391182],
                          [ 0.8           ,  0.8           ,  0.167775391182],
                          [ 0.1           ,  0.            ,  0.178261353131],
                          [ 0.3           ,  0.            ,  0.178261353131],
                          [ 0.5           ,  0.            ,  0.178261353131],
                          [ 0.7           ,  0.            ,  0.178261353131],
                          [ 0.9           ,  0.            ,  0.178261353131],
                          [ 0.1           ,  0.2           ,  0.178261353131],
                          [ 0.3           ,  0.2           ,  0.178261353131],
                          [ 0.5           ,  0.2           ,  0.178261353131],
                          [ 0.7           ,  0.2           ,  0.178261353131],
                          [ 0.9           ,  0.2           ,  0.178261353131],
                          [ 0.1           ,  0.4           ,  0.178261353131],
                          [ 0.3           ,  0.4           ,  0.178261353131],
                          [ 0.5           ,  0.4           ,  0.178261353131],
                          [ 0.7           ,  0.4           ,  0.178261353131],
                          [ 0.9           ,  0.4           ,  0.178261353131],
                          [ 0.1           ,  0.6           ,  0.178261353131],
                          [ 0.3           ,  0.6           ,  0.178261353131],
                          [ 0.5           ,  0.6           ,  0.178261353131],
                          [ 0.7           ,  0.6           ,  0.178261353131],
                          [ 0.9           ,  0.6           ,  0.178261353131],
                          [ 0.1           ,  0.8           ,  0.178261353131],
                          [ 0.3           ,  0.8           ,  0.178261353131],
                          [ 0.5           ,  0.8           ,  0.178261353131],
                          [ 0.7           ,  0.8           ,  0.178261353131],
                          [ 0.9           ,  0.8           ,  0.178261353131],
                          [ 0.1           ,  0.1           ,  0.18874731508 ],
                          [ 0.3           ,  0.1           ,  0.18874731508 ],
                          [ 0.5           ,  0.1           ,  0.18874731508 ],
                          [ 0.7           ,  0.1           ,  0.18874731508 ],
                          [ 0.9           ,  0.1           ,  0.18874731508 ],
                          [ 0.1           ,  0.3           ,  0.18874731508 ],
                          [ 0.3           ,  0.3           ,  0.18874731508 ],
                          [ 0.5           ,  0.3           ,  0.18874731508 ],
                          [ 0.7           ,  0.3           ,  0.18874731508 ],
                          [ 0.9           ,  0.3           ,  0.18874731508 ],
                          [ 0.1           ,  0.5           ,  0.18874731508 ],
                          [ 0.3           ,  0.5           ,  0.18874731508 ],
                          [ 0.5           ,  0.5           ,  0.18874731508 ],
                          [ 0.7           ,  0.5           ,  0.18874731508 ],
                          [ 0.9           ,  0.5           ,  0.18874731508 ],
                          [ 0.1           ,  0.7           ,  0.18874731508 ],
                          [ 0.3           ,  0.7           ,  0.18874731508 ],
                          [ 0.5           ,  0.7           ,  0.18874731508 ],
                          [ 0.7           ,  0.7           ,  0.18874731508 ],
                          [ 0.9           ,  0.7           ,  0.18874731508 ],
                          [ 0.1           ,  0.9           ,  0.18874731508 ],
                          [ 0.3           ,  0.9           ,  0.18874731508 ],
                          [ 0.5           ,  0.9           ,  0.18874731508 ],
                          [ 0.7           ,  0.9           ,  0.18874731508 ],
                          [ 0.9           ,  0.9           ,  0.18874731508 ],
                          [ 0.            ,  0.1           ,  0.199233277029],
                          [ 0.2           ,  0.1           ,  0.199233277029],
                          [ 0.4           ,  0.1           ,  0.199233277029],
                          [ 0.6           ,  0.1           ,  0.199233277029],
                          [ 0.8           ,  0.1           ,  0.199233277029],
                          [ 0.            ,  0.3           ,  0.199233277029],
                          [ 0.2           ,  0.3           ,  0.199233277029],
                          [ 0.4           ,  0.3           ,  0.199233277029],
                          [ 0.6           ,  0.3           ,  0.199233277029],
                          [ 0.8           ,  0.3           ,  0.199233277029],
                          [ 0.            ,  0.5           ,  0.199233277029],
                          [ 0.2           ,  0.5           ,  0.199233277029],
                          [ 0.4           ,  0.5           ,  0.199233277029],
                          [ 0.6           ,  0.5           ,  0.199233277029],
                          [ 0.8           ,  0.5           ,  0.199233277029],
                          [ 0.            ,  0.7           ,  0.199233277029],
                          [ 0.2           ,  0.7           ,  0.199233277029],
                          [ 0.4           ,  0.7           ,  0.199233277029],
                          [ 0.6           ,  0.7           ,  0.199233277029],
                          [ 0.8           ,  0.7           ,  0.199233277029],
                          [ 0.            ,  0.9           ,  0.199233277029],
                          [ 0.2           ,  0.9           ,  0.199233277029],
                          [ 0.4           ,  0.9           ,  0.199233277029],
                          [ 0.6           ,  0.9           ,  0.199233277029],
                          [ 0.8           ,  0.9           ,  0.199233277029],
                          [ 0.            ,  0.            ,  0.209719238977],
                          [ 0.2           ,  0.            ,  0.209719238977],
                          [ 0.4           ,  0.            ,  0.209719238977],
                          [ 0.6           ,  0.            ,  0.209719238977],
                          [ 0.8           ,  0.            ,  0.209719238977],
                          [ 0.            ,  0.2           ,  0.209719238977],
                          [ 0.2           ,  0.2           ,  0.209719238977],
                          [ 0.4           ,  0.2           ,  0.209719238977],
                          [ 0.6           ,  0.2           ,  0.209719238977],
                          [ 0.8           ,  0.2           ,  0.209719238977],
                          [ 0.            ,  0.4           ,  0.209719238977],
                          [ 0.2           ,  0.4           ,  0.209719238977],
                          [ 0.4           ,  0.4           ,  0.209719238977],
                          [ 0.6           ,  0.4           ,  0.209719238977],
                          [ 0.8           ,  0.4           ,  0.209719238977],
                          [ 0.            ,  0.6           ,  0.209719238977],
                          [ 0.2           ,  0.6           ,  0.209719238977],
                          [ 0.4           ,  0.6           ,  0.209719238977],
                          [ 0.6           ,  0.6           ,  0.209719238977],
                          [ 0.8           ,  0.6           ,  0.209719238977],
                          [ 0.            ,  0.8           ,  0.209719238977],
                          [ 0.2           ,  0.8           ,  0.209719238977],
                          [ 0.4           ,  0.8           ,  0.209719238977],
                          [ 0.6           ,  0.8           ,  0.209719238977],
                          [ 0.8           ,  0.8           ,  0.209719238977],
                          [ 0.1           ,  0.            ,  0.220205200926],
                          [ 0.3           ,  0.            ,  0.220205200926],
                          [ 0.5           ,  0.            ,  0.220205200926],
                          [ 0.7           ,  0.            ,  0.220205200926],
                          [ 0.9           ,  0.            ,  0.220205200926],
                          [ 0.1           ,  0.2           ,  0.220205200926],
                          [ 0.3           ,  0.2           ,  0.220205200926],
                          [ 0.5           ,  0.2           ,  0.220205200926],
                          [ 0.7           ,  0.2           ,  0.220205200926],
                          [ 0.9           ,  0.2           ,  0.220205200926],
                          [ 0.1           ,  0.4           ,  0.220205200926],
                          [ 0.3           ,  0.4           ,  0.220205200926],
                          [ 0.5           ,  0.4           ,  0.220205200926],
                          [ 0.7           ,  0.4           ,  0.220205200926],
                          [ 0.9           ,  0.4           ,  0.220205200926],
                          [ 0.1           ,  0.6           ,  0.220205200926],
                          [ 0.3           ,  0.6           ,  0.220205200926],
                          [ 0.5           ,  0.6           ,  0.220205200926],
                          [ 0.7           ,  0.6           ,  0.220205200926],
                          [ 0.9           ,  0.6           ,  0.220205200926],
                          [ 0.1           ,  0.8           ,  0.220205200926],
                          [ 0.3           ,  0.8           ,  0.220205200926],
                          [ 0.5           ,  0.8           ,  0.220205200926],
                          [ 0.7           ,  0.8           ,  0.220205200926],
                          [ 0.9           ,  0.8           ,  0.220205200926],
                          [ 0.1           ,  0.1           ,  0.230691162875],
                          [ 0.3           ,  0.1           ,  0.230691162875],
                          [ 0.5           ,  0.1           ,  0.230691162875],
                          [ 0.7           ,  0.1           ,  0.230691162875],
                          [ 0.9           ,  0.1           ,  0.230691162875],
                          [ 0.1           ,  0.3           ,  0.230691162875],
                          [ 0.3           ,  0.3           ,  0.230691162875],
                          [ 0.5           ,  0.3           ,  0.230691162875],
                          [ 0.7           ,  0.3           ,  0.230691162875],
                          [ 0.9           ,  0.3           ,  0.230691162875],
                          [ 0.1           ,  0.5           ,  0.230691162875],
                          [ 0.3           ,  0.5           ,  0.230691162875],
                          [ 0.5           ,  0.5           ,  0.230691162875],
                          [ 0.7           ,  0.5           ,  0.230691162875],
                          [ 0.9           ,  0.5           ,  0.230691162875],
                          [ 0.1           ,  0.7           ,  0.230691162875],
                          [ 0.3           ,  0.7           ,  0.230691162875],
                          [ 0.5           ,  0.7           ,  0.230691162875],
                          [ 0.7           ,  0.7           ,  0.230691162875],
                          [ 0.9           ,  0.7           ,  0.230691162875],
                          [ 0.1           ,  0.9           ,  0.230691162875],
                          [ 0.3           ,  0.9           ,  0.230691162875],
                          [ 0.5           ,  0.9           ,  0.230691162875],
                          [ 0.7           ,  0.9           ,  0.230691162875],
                          [ 0.9           ,  0.9           ,  0.230691162875],
                          [ 0.            ,  0.1           ,  0.241177124824],
                          [ 0.2           ,  0.1           ,  0.241177124824],
                          [ 0.4           ,  0.1           ,  0.241177124824],
                          [ 0.6           ,  0.1           ,  0.241177124824],
                          [ 0.8           ,  0.1           ,  0.241177124824],
                          [ 0.            ,  0.3           ,  0.241177124824],
                          [ 0.2           ,  0.3           ,  0.241177124824],
                          [ 0.4           ,  0.3           ,  0.241177124824],
                          [ 0.6           ,  0.3           ,  0.241177124824],
                          [ 0.8           ,  0.3           ,  0.241177124824],
                          [ 0.            ,  0.5           ,  0.241177124824],
                          [ 0.2           ,  0.5           ,  0.241177124824],
                          [ 0.4           ,  0.5           ,  0.241177124824],
                          [ 0.6           ,  0.5           ,  0.241177124824],
                          [ 0.8           ,  0.5           ,  0.241177124824],
                          [ 0.            ,  0.7           ,  0.241177124824],
                          [ 0.2           ,  0.7           ,  0.241177124824],
                          [ 0.4           ,  0.7           ,  0.241177124824],
                          [ 0.6           ,  0.7           ,  0.241177124824],
                          [ 0.8           ,  0.7           ,  0.241177124824],
                          [ 0.            ,  0.9           ,  0.241177124824],
                          [ 0.2           ,  0.9           ,  0.241177124824],
                          [ 0.4           ,  0.9           ,  0.241177124824],
                          [ 0.6           ,  0.9           ,  0.241177124824],
                          [ 0.8           ,  0.9           ,  0.241177124824],
                          [ 0.            ,  0.            ,  0.251663086773],
                          [ 0.2           ,  0.            ,  0.251663086773],
                          [ 0.4           ,  0.            ,  0.251663086773],
                          [ 0.6           ,  0.            ,  0.251663086773],
                          [ 0.8           ,  0.            ,  0.251663086773],
                          [ 0.            ,  0.2           ,  0.251663086773],
                          [ 0.2           ,  0.2           ,  0.251663086773],
                          [ 0.4           ,  0.2           ,  0.251663086773],
                          [ 0.6           ,  0.2           ,  0.251663086773],
                          [ 0.8           ,  0.2           ,  0.251663086773],
                          [ 0.            ,  0.4           ,  0.251663086773],
                          [ 0.2           ,  0.4           ,  0.251663086773],
                          [ 0.4           ,  0.4           ,  0.251663086773],
                          [ 0.6           ,  0.4           ,  0.251663086773],
                          [ 0.8           ,  0.4           ,  0.251663086773],
                          [ 0.            ,  0.6           ,  0.251663086773],
                          [ 0.2           ,  0.6           ,  0.251663086773],
                          [ 0.4           ,  0.6           ,  0.251663086773],
                          [ 0.6           ,  0.6           ,  0.251663086773],
                          [ 0.8           ,  0.6           ,  0.251663086773],
                          [ 0.            ,  0.8           ,  0.251663086773],
                          [ 0.2           ,  0.8           ,  0.251663086773],
                          [ 0.4           ,  0.8           ,  0.251663086773],
                          [ 0.6           ,  0.8           ,  0.251663086773],
                          [ 0.8           ,  0.8           ,  0.251663086773],
                          [ 0.1           ,  0.            ,  0.262149048722],
                          [ 0.3           ,  0.            ,  0.262149048722],
                          [ 0.5           ,  0.            ,  0.262149048722],
                          [ 0.7           ,  0.            ,  0.262149048722],
                          [ 0.9           ,  0.            ,  0.262149048722],
                          [ 0.1           ,  0.2           ,  0.262149048722],
                          [ 0.3           ,  0.2           ,  0.262149048722],
                          [ 0.5           ,  0.2           ,  0.262149048722],
                          [ 0.7           ,  0.2           ,  0.262149048722],
                          [ 0.9           ,  0.2           ,  0.262149048722],
                          [ 0.1           ,  0.4           ,  0.262149048722],
                          [ 0.3           ,  0.4           ,  0.262149048722],
                          [ 0.5           ,  0.4           ,  0.262149048722],
                          [ 0.7           ,  0.4           ,  0.262149048722],
                          [ 0.9           ,  0.4           ,  0.262149048722],
                          [ 0.1           ,  0.6           ,  0.262149048722],
                          [ 0.3           ,  0.6           ,  0.262149048722],
                          [ 0.5           ,  0.6           ,  0.262149048722],
                          [ 0.7           ,  0.6           ,  0.262149048722],
                          [ 0.9           ,  0.6           ,  0.262149048722],
                          [ 0.1           ,  0.8           ,  0.262149048722],
                          [ 0.3           ,  0.8           ,  0.262149048722],
                          [ 0.5           ,  0.8           ,  0.262149048722],
                          [ 0.7           ,  0.8           ,  0.262149048722],
                          [ 0.9           ,  0.8           ,  0.262149048722],
                          [ 0.1           ,  0.1           ,  0.272635010671],
                          [ 0.3           ,  0.1           ,  0.272635010671],
                          [ 0.5           ,  0.1           ,  0.272635010671],
                          [ 0.7           ,  0.1           ,  0.272635010671],
                          [ 0.9           ,  0.1           ,  0.272635010671],
                          [ 0.1           ,  0.3           ,  0.272635010671],
                          [ 0.3           ,  0.3           ,  0.272635010671],
                          [ 0.5           ,  0.3           ,  0.272635010671],
                          [ 0.7           ,  0.3           ,  0.272635010671],
                          [ 0.9           ,  0.3           ,  0.272635010671],
                          [ 0.1           ,  0.5           ,  0.272635010671],
                          [ 0.3           ,  0.5           ,  0.272635010671],
                          [ 0.5           ,  0.5           ,  0.272635010671],
                          [ 0.7           ,  0.5           ,  0.272635010671],
                          [ 0.9           ,  0.5           ,  0.272635010671],
                          [ 0.1           ,  0.7           ,  0.272635010671],
                          [ 0.3           ,  0.7           ,  0.272635010671],
                          [ 0.5           ,  0.7           ,  0.272635010671],
                          [ 0.7           ,  0.7           ,  0.272635010671],
                          [ 0.9           ,  0.7           ,  0.272635010671],
                          [ 0.1           ,  0.9           ,  0.272635010671],
                          [ 0.3           ,  0.9           ,  0.272635010671],
                          [ 0.5           ,  0.9           ,  0.272635010671],
                          [ 0.7           ,  0.9           ,  0.272635010671],
                          [ 0.9           ,  0.9           ,  0.272635010671],
                          [ 0.            ,  0.1           ,  0.283120972619],
                          [ 0.2           ,  0.1           ,  0.283120972619],
                          [ 0.4           ,  0.1           ,  0.283120972619],
                          [ 0.6           ,  0.1           ,  0.283120972619],
                          [ 0.8           ,  0.1           ,  0.283120972619],
                          [ 0.            ,  0.3           ,  0.283120972619],
                          [ 0.2           ,  0.3           ,  0.283120972619],
                          [ 0.4           ,  0.3           ,  0.283120972619],
                          [ 0.6           ,  0.3           ,  0.283120972619],
                          [ 0.8           ,  0.3           ,  0.283120972619],
                          [ 0.            ,  0.5           ,  0.283120972619],
                          [ 0.2           ,  0.5           ,  0.283120972619],
                          [ 0.4           ,  0.5           ,  0.283120972619],
                          [ 0.6           ,  0.5           ,  0.283120972619],
                          [ 0.8           ,  0.5           ,  0.283120972619],
                          [ 0.            ,  0.7           ,  0.283120972619],
                          [ 0.2           ,  0.7           ,  0.283120972619],
                          [ 0.4           ,  0.7           ,  0.283120972619],
                          [ 0.6           ,  0.7           ,  0.283120972619],
                          [ 0.8           ,  0.7           ,  0.283120972619],
                          [ 0.            ,  0.9           ,  0.283120972619],
                          [ 0.2           ,  0.9           ,  0.283120972619],
                          [ 0.4           ,  0.9           ,  0.283120972619],
                          [ 0.6           ,  0.9           ,  0.283120972619],
                          [ 0.8           ,  0.9           ,  0.283120972619],
                          [ 0.            ,  0.            ,  0.293606934568],
                          [ 0.2           ,  0.            ,  0.293606934568],
                          [ 0.4           ,  0.            ,  0.293606934568],
                          [ 0.6           ,  0.            ,  0.293606934568],
                          [ 0.8           ,  0.            ,  0.293606934568],
                          [ 0.            ,  0.2           ,  0.293606934568],
                          [ 0.2           ,  0.2           ,  0.293606934568],
                          [ 0.4           ,  0.2           ,  0.293606934568],
                          [ 0.6           ,  0.2           ,  0.293606934568],
                          [ 0.8           ,  0.2           ,  0.293606934568],
                          [ 0.            ,  0.4           ,  0.293606934568],
                          [ 0.2           ,  0.4           ,  0.293606934568],
                          [ 0.4           ,  0.4           ,  0.293606934568],
                          [ 0.6           ,  0.4           ,  0.293606934568],
                          [ 0.8           ,  0.4           ,  0.293606934568],
                          [ 0.            ,  0.6           ,  0.293606934568],
                          [ 0.2           ,  0.6           ,  0.293606934568],
                          [ 0.4           ,  0.6           ,  0.293606934568],
                          [ 0.6           ,  0.6           ,  0.293606934568],
                          [ 0.8           ,  0.6           ,  0.293606934568],
                          [ 0.            ,  0.8           ,  0.293606934568],
                          [ 0.2           ,  0.8           ,  0.293606934568],
                          [ 0.4           ,  0.8           ,  0.293606934568],
                          [ 0.6           ,  0.8           ,  0.293606934568],
                          [ 0.8           ,  0.8           ,  0.293606934568],
                          [ 0.1           ,  0.            ,  0.304092896517],
                          [ 0.3           ,  0.            ,  0.304092896517],
                          [ 0.5           ,  0.            ,  0.304092896517],
                          [ 0.7           ,  0.            ,  0.304092896517],
                          [ 0.9           ,  0.            ,  0.304092896517],
                          [ 0.1           ,  0.2           ,  0.304092896517],
                          [ 0.3           ,  0.2           ,  0.304092896517],
                          [ 0.5           ,  0.2           ,  0.304092896517],
                          [ 0.7           ,  0.2           ,  0.304092896517],
                          [ 0.9           ,  0.2           ,  0.304092896517],
                          [ 0.1           ,  0.4           ,  0.304092896517],
                          [ 0.3           ,  0.4           ,  0.304092896517],
                          [ 0.5           ,  0.4           ,  0.304092896517],
                          [ 0.7           ,  0.4           ,  0.304092896517],
                          [ 0.9           ,  0.4           ,  0.304092896517],
                          [ 0.1           ,  0.6           ,  0.304092896517],
                          [ 0.3           ,  0.6           ,  0.304092896517],
                          [ 0.5           ,  0.6           ,  0.304092896517],
                          [ 0.7           ,  0.6           ,  0.304092896517],
                          [ 0.9           ,  0.6           ,  0.304092896517],
                          [ 0.1           ,  0.8           ,  0.304092896517],
                          [ 0.3           ,  0.8           ,  0.304092896517],
                          [ 0.5           ,  0.8           ,  0.304092896517],
                          [ 0.7           ,  0.8           ,  0.304092896517],
                          [ 0.9           ,  0.8           ,  0.304092896517],
                          [ 0.1           ,  0.1           ,  0.314578858466],
                          [ 0.3           ,  0.1           ,  0.314578858466],
                          [ 0.5           ,  0.1           ,  0.314578858466],
                          [ 0.7           ,  0.1           ,  0.314578858466],
                          [ 0.9           ,  0.1           ,  0.314578858466],
                          [ 0.1           ,  0.3           ,  0.314578858466],
                          [ 0.3           ,  0.3           ,  0.314578858466],
                          [ 0.5           ,  0.3           ,  0.314578858466],
                          [ 0.7           ,  0.3           ,  0.314578858466],
                          [ 0.9           ,  0.3           ,  0.314578858466],
                          [ 0.1           ,  0.5           ,  0.314578858466],
                          [ 0.3           ,  0.5           ,  0.314578858466],
                          [ 0.5           ,  0.5           ,  0.314578858466],
                          [ 0.7           ,  0.5           ,  0.314578858466],
                          [ 0.9           ,  0.5           ,  0.314578858466],
                          [ 0.1           ,  0.7           ,  0.314578858466],
                          [ 0.3           ,  0.7           ,  0.314578858466],
                          [ 0.5           ,  0.7           ,  0.314578858466],
                          [ 0.7           ,  0.7           ,  0.314578858466],
                          [ 0.9           ,  0.7           ,  0.314578858466],
                          [ 0.1           ,  0.9           ,  0.314578858466],
                          [ 0.3           ,  0.9           ,  0.314578858466],
                          [ 0.5           ,  0.9           ,  0.314578858466],
                          [ 0.7           ,  0.9           ,  0.314578858466],
                          [ 0.9           ,  0.9           ,  0.314578858466],
                          [ 0.            ,  0.1           ,  0.325064820415],
                          [ 0.2           ,  0.1           ,  0.325064820415],
                          [ 0.4           ,  0.1           ,  0.325064820415],
                          [ 0.6           ,  0.1           ,  0.325064820415],
                          [ 0.8           ,  0.1           ,  0.325064820415],
                          [ 0.            ,  0.3           ,  0.325064820415],
                          [ 0.2           ,  0.3           ,  0.325064820415],
                          [ 0.4           ,  0.3           ,  0.325064820415],
                          [ 0.6           ,  0.3           ,  0.325064820415],
                          [ 0.8           ,  0.3           ,  0.325064820415],
                          [ 0.            ,  0.5           ,  0.325064820415],
                          [ 0.2           ,  0.5           ,  0.325064820415],
                          [ 0.4           ,  0.5           ,  0.325064820415],
                          [ 0.6           ,  0.5           ,  0.325064820415],
                          [ 0.8           ,  0.5           ,  0.325064820415],
                          [ 0.            ,  0.7           ,  0.325064820415],
                          [ 0.2           ,  0.7           ,  0.325064820415],
                          [ 0.4           ,  0.7           ,  0.325064820415],
                          [ 0.6           ,  0.7           ,  0.325064820415],
                          [ 0.8           ,  0.7           ,  0.325064820415],
                          [ 0.            ,  0.9           ,  0.325064820415],
                          [ 0.2           ,  0.9           ,  0.325064820415],
                          [ 0.4           ,  0.9           ,  0.325064820415],
                          [ 0.6           ,  0.9           ,  0.325064820415],
                          [ 0.8           ,  0.9           ,  0.325064820415],
                          [ 0.            ,  0.            ,  0.335550782364],
                          [ 0.2           ,  0.            ,  0.335550782364],
                          [ 0.4           ,  0.            ,  0.335550782364],
                          [ 0.6           ,  0.            ,  0.335550782364],
                          [ 0.8           ,  0.            ,  0.335550782364],
                          [ 0.            ,  0.2           ,  0.335550782364],
                          [ 0.2           ,  0.2           ,  0.335550782364],
                          [ 0.4           ,  0.2           ,  0.335550782364],
                          [ 0.6           ,  0.2           ,  0.335550782364],
                          [ 0.8           ,  0.2           ,  0.335550782364],
                          [ 0.            ,  0.4           ,  0.335550782364],
                          [ 0.2           ,  0.4           ,  0.335550782364],
                          [ 0.4           ,  0.4           ,  0.335550782364],
                          [ 0.6           ,  0.4           ,  0.335550782364],
                          [ 0.8           ,  0.4           ,  0.335550782364],
                          [ 0.            ,  0.6           ,  0.335550782364],
                          [ 0.2           ,  0.6           ,  0.335550782364],
                          [ 0.4           ,  0.6           ,  0.335550782364],
                          [ 0.6           ,  0.6           ,  0.335550782364],
                          [ 0.8           ,  0.6           ,  0.335550782364],
                          [ 0.            ,  0.8           ,  0.335550782364],
                          [ 0.2           ,  0.8           ,  0.335550782364],
                          [ 0.4           ,  0.8           ,  0.335550782364],
                          [ 0.6           ,  0.8           ,  0.335550782364],
                          [ 0.8           ,  0.8           ,  0.335550782364],
                          [ 0.1           ,  0.            ,  0.346036744313],
                          [ 0.3           ,  0.            ,  0.346036744313],
                          [ 0.5           ,  0.            ,  0.346036744313],
                          [ 0.7           ,  0.            ,  0.346036744313],
                          [ 0.9           ,  0.            ,  0.346036744313],
                          [ 0.1           ,  0.2           ,  0.346036744313],
                          [ 0.3           ,  0.2           ,  0.346036744313],
                          [ 0.5           ,  0.2           ,  0.346036744313],
                          [ 0.7           ,  0.2           ,  0.346036744313],
                          [ 0.9           ,  0.2           ,  0.346036744313],
                          [ 0.1           ,  0.4           ,  0.346036744313],
                          [ 0.3           ,  0.4           ,  0.346036744313],
                          [ 0.5           ,  0.4           ,  0.346036744313],
                          [ 0.7           ,  0.4           ,  0.346036744313],
                          [ 0.9           ,  0.4           ,  0.346036744313],
                          [ 0.1           ,  0.6           ,  0.346036744313],
                          [ 0.3           ,  0.6           ,  0.346036744313],
                          [ 0.5           ,  0.6           ,  0.346036744313],
                          [ 0.7           ,  0.6           ,  0.346036744313],
                          [ 0.9           ,  0.6           ,  0.346036744313],
                          [ 0.1           ,  0.8           ,  0.346036744313],
                          [ 0.3           ,  0.8           ,  0.346036744313],
                          [ 0.5           ,  0.8           ,  0.346036744313],
                          [ 0.7           ,  0.8           ,  0.346036744313],
                          [ 0.9           ,  0.8           ,  0.346036744313],
                          [ 0.1           ,  0.1           ,  0.356522706261],
                          [ 0.3           ,  0.1           ,  0.356522706261],
                          [ 0.5           ,  0.1           ,  0.356522706261],
                          [ 0.7           ,  0.1           ,  0.356522706261],
                          [ 0.9           ,  0.1           ,  0.356522706261],
                          [ 0.1           ,  0.3           ,  0.356522706261],
                          [ 0.3           ,  0.3           ,  0.356522706261],
                          [ 0.5           ,  0.3           ,  0.356522706261],
                          [ 0.7           ,  0.3           ,  0.356522706261],
                          [ 0.9           ,  0.3           ,  0.356522706261],
                          [ 0.1           ,  0.5           ,  0.356522706261],
                          [ 0.3           ,  0.5           ,  0.356522706261],
                          [ 0.5           ,  0.5           ,  0.356522706261],
                          [ 0.7           ,  0.5           ,  0.356522706261],
                          [ 0.9           ,  0.5           ,  0.356522706261],
                          [ 0.1           ,  0.7           ,  0.356522706261],
                          [ 0.3           ,  0.7           ,  0.356522706261],
                          [ 0.5           ,  0.7           ,  0.356522706261],
                          [ 0.7           ,  0.7           ,  0.356522706261],
                          [ 0.9           ,  0.7           ,  0.356522706261],
                          [ 0.1           ,  0.9           ,  0.356522706261],
                          [ 0.3           ,  0.9           ,  0.356522706261],
                          [ 0.5           ,  0.9           ,  0.356522706261],
                          [ 0.7           ,  0.9           ,  0.356522706261],
                          [ 0.9           ,  0.9           ,  0.356522706261],
                          [ 0.            ,  0.1           ,  0.36700866821 ],
                          [ 0.2           ,  0.1           ,  0.36700866821 ],
                          [ 0.4           ,  0.1           ,  0.36700866821 ],
                          [ 0.6           ,  0.1           ,  0.36700866821 ],
                          [ 0.8           ,  0.1           ,  0.36700866821 ],
                          [ 0.            ,  0.3           ,  0.36700866821 ],
                          [ 0.2           ,  0.3           ,  0.36700866821 ],
                          [ 0.4           ,  0.3           ,  0.36700866821 ],
                          [ 0.6           ,  0.3           ,  0.36700866821 ],
                          [ 0.8           ,  0.3           ,  0.36700866821 ],
                          [ 0.            ,  0.5           ,  0.36700866821 ],
                          [ 0.2           ,  0.5           ,  0.36700866821 ],
                          [ 0.4           ,  0.5           ,  0.36700866821 ],
                          [ 0.6           ,  0.5           ,  0.36700866821 ],
                          [ 0.8           ,  0.5           ,  0.36700866821 ],
                          [ 0.            ,  0.7           ,  0.36700866821 ],
                          [ 0.2           ,  0.7           ,  0.36700866821 ],
                          [ 0.4           ,  0.7           ,  0.36700866821 ],
                          [ 0.6           ,  0.7           ,  0.36700866821 ],
                          [ 0.8           ,  0.7           ,  0.36700866821 ],
                          [ 0.            ,  0.9           ,  0.36700866821 ],
                          [ 0.2           ,  0.9           ,  0.36700866821 ],
                          [ 0.4           ,  0.9           ,  0.36700866821 ],
                          [ 0.6           ,  0.9           ,  0.36700866821 ],
                          [ 0.8           ,  0.9           ,  0.36700866821 ],
                          [ 0.            ,  0.            ,  0.377494630159],
                          [ 0.2           ,  0.            ,  0.377494630159],
                          [ 0.4           ,  0.            ,  0.377494630159],
                          [ 0.6           ,  0.            ,  0.377494630159],
                          [ 0.8           ,  0.            ,  0.377494630159],
                          [ 0.            ,  0.2           ,  0.377494630159],
                          [ 0.2           ,  0.2           ,  0.377494630159],
                          [ 0.4           ,  0.2           ,  0.377494630159],
                          [ 0.6           ,  0.2           ,  0.377494630159],
                          [ 0.8           ,  0.2           ,  0.377494630159],
                          [ 0.            ,  0.4           ,  0.377494630159],
                          [ 0.2           ,  0.4           ,  0.377494630159],
                          [ 0.4           ,  0.4           ,  0.377494630159],
                          [ 0.6           ,  0.4           ,  0.377494630159],
                          [ 0.8           ,  0.4           ,  0.377494630159],
                          [ 0.            ,  0.6           ,  0.377494630159],
                          [ 0.2           ,  0.6           ,  0.377494630159],
                          [ 0.4           ,  0.6           ,  0.377494630159],
                          [ 0.6           ,  0.6           ,  0.377494630159],
                          [ 0.8           ,  0.6           ,  0.377494630159],
                          [ 0.            ,  0.8           ,  0.377494630159],
                          [ 0.2           ,  0.8           ,  0.377494630159],
                          [ 0.4           ,  0.8           ,  0.377494630159],
                          [ 0.6           ,  0.8           ,  0.377494630159],
                          [ 0.8           ,  0.8           ,  0.377494630159],
                          [ 0.1           ,  0.            ,  0.387980592108],
                          [ 0.3           ,  0.            ,  0.387980592108],
                          [ 0.5           ,  0.            ,  0.387980592108],
                          [ 0.7           ,  0.            ,  0.387980592108],
                          [ 0.9           ,  0.            ,  0.387980592108],
                          [ 0.1           ,  0.2           ,  0.387980592108],
                          [ 0.3           ,  0.2           ,  0.387980592108],
                          [ 0.5           ,  0.2           ,  0.387980592108],
                          [ 0.7           ,  0.2           ,  0.387980592108],
                          [ 0.9           ,  0.2           ,  0.387980592108],
                          [ 0.1           ,  0.4           ,  0.387980592108],
                          [ 0.3           ,  0.4           ,  0.387980592108],
                          [ 0.5           ,  0.4           ,  0.387980592108],
                          [ 0.7           ,  0.4           ,  0.387980592108],
                          [ 0.9           ,  0.4           ,  0.387980592108],
                          [ 0.1           ,  0.6           ,  0.387980592108],
                          [ 0.3           ,  0.6           ,  0.387980592108],
                          [ 0.5           ,  0.6           ,  0.387980592108],
                          [ 0.7           ,  0.6           ,  0.387980592108],
                          [ 0.9           ,  0.6           ,  0.387980592108],
                          [ 0.1           ,  0.8           ,  0.387980592108],
                          [ 0.3           ,  0.8           ,  0.387980592108],
                          [ 0.5           ,  0.8           ,  0.387980592108],
                          [ 0.7           ,  0.8           ,  0.387980592108],
                          [ 0.9           ,  0.8           ,  0.387980592108],
                          [ 0.1           ,  0.1           ,  0.398466554057],
                          [ 0.3           ,  0.1           ,  0.398466554057],
                          [ 0.5           ,  0.1           ,  0.398466554057],
                          [ 0.7           ,  0.1           ,  0.398466554057],
                          [ 0.9           ,  0.1           ,  0.398466554057],
                          [ 0.1           ,  0.3           ,  0.398466554057],
                          [ 0.3           ,  0.3           ,  0.398466554057],
                          [ 0.5           ,  0.3           ,  0.398466554057],
                          [ 0.7           ,  0.3           ,  0.398466554057],
                          [ 0.9           ,  0.3           ,  0.398466554057],
                          [ 0.1           ,  0.5           ,  0.398466554057],
                          [ 0.3           ,  0.5           ,  0.398466554057],
                          [ 0.5           ,  0.5           ,  0.398466554057],
                          [ 0.7           ,  0.5           ,  0.398466554057],
                          [ 0.9           ,  0.5           ,  0.398466554057],
                          [ 0.1           ,  0.7           ,  0.398466554057],
                          [ 0.3           ,  0.7           ,  0.398466554057],
                          [ 0.5           ,  0.7           ,  0.398466554057],
                          [ 0.7           ,  0.7           ,  0.398466554057],
                          [ 0.9           ,  0.7           ,  0.398466554057],
                          [ 0.1           ,  0.9           ,  0.398466554057],
                          [ 0.3           ,  0.9           ,  0.398466554057],
                          [ 0.5           ,  0.9           ,  0.398466554057],
                          [ 0.7           ,  0.9           ,  0.398466554057],
                          [ 0.9           ,  0.9           ,  0.398466554057],
                          [ 0.            ,  0.1           ,  0.408952516006],
                          [ 0.2           ,  0.1           ,  0.408952516006],
                          [ 0.4           ,  0.1           ,  0.408952516006],
                          [ 0.6           ,  0.1           ,  0.408952516006],
                          [ 0.8           ,  0.1           ,  0.408952516006],
                          [ 0.            ,  0.3           ,  0.408952516006],
                          [ 0.2           ,  0.3           ,  0.408952516006],
                          [ 0.4           ,  0.3           ,  0.408952516006],
                          [ 0.6           ,  0.3           ,  0.408952516006],
                          [ 0.8           ,  0.3           ,  0.408952516006],
                          [ 0.            ,  0.5           ,  0.408952516006],
                          [ 0.2           ,  0.5           ,  0.408952516006],
                          [ 0.4           ,  0.5           ,  0.408952516006],
                          [ 0.6           ,  0.5           ,  0.408952516006],
                          [ 0.8           ,  0.5           ,  0.408952516006],
                          [ 0.            ,  0.7           ,  0.408952516006],
                          [ 0.2           ,  0.7           ,  0.408952516006],
                          [ 0.4           ,  0.7           ,  0.408952516006],
                          [ 0.6           ,  0.7           ,  0.408952516006],
                          [ 0.8           ,  0.7           ,  0.408952516006],
                          [ 0.            ,  0.9           ,  0.408952516006],
                          [ 0.2           ,  0.9           ,  0.408952516006],
                          [ 0.4           ,  0.9           ,  0.408952516006],
                          [ 0.6           ,  0.9           ,  0.408952516006],
                          [ 0.8           ,  0.9           ,  0.408952516006],
                          [ 0.            ,  0.            ,  0.419438477955],
                          [ 0.2           ,  0.            ,  0.419438477955],
                          [ 0.4           ,  0.            ,  0.419438477955],
                          [ 0.6           ,  0.            ,  0.419438477955],
                          [ 0.8           ,  0.            ,  0.419438477955],
                          [ 0.            ,  0.2           ,  0.419438477955],
                          [ 0.2           ,  0.2           ,  0.419438477955],
                          [ 0.4           ,  0.2           ,  0.419438477955],
                          [ 0.6           ,  0.2           ,  0.419438477955],
                          [ 0.8           ,  0.2           ,  0.419438477955],
                          [ 0.            ,  0.4           ,  0.419438477955],
                          [ 0.2           ,  0.4           ,  0.419438477955],
                          [ 0.4           ,  0.4           ,  0.419438477955],
                          [ 0.6           ,  0.4           ,  0.419438477955],
                          [ 0.8           ,  0.4           ,  0.419438477955],
                          [ 0.            ,  0.6           ,  0.419438477955],
                          [ 0.2           ,  0.6           ,  0.419438477955],
                          [ 0.4           ,  0.6           ,  0.419438477955],
                          [ 0.6           ,  0.6           ,  0.419438477955],
                          [ 0.8           ,  0.6           ,  0.419438477955],
                          [ 0.            ,  0.8           ,  0.419438477955],
                          [ 0.2           ,  0.8           ,  0.419438477955],
                          [ 0.4           ,  0.8           ,  0.419438477955],
                          [ 0.6           ,  0.8           ,  0.419438477955],
                          [ 0.8           ,  0.8           ,  0.419438477955],
                          [ 0.1           ,  0.            ,  0.429924439903],
                          [ 0.3           ,  0.            ,  0.429924439903],
                          [ 0.5           ,  0.            ,  0.429924439903],
                          [ 0.7           ,  0.            ,  0.429924439903],
                          [ 0.9           ,  0.            ,  0.429924439903],
                          [ 0.1           ,  0.2           ,  0.429924439903],
                          [ 0.3           ,  0.2           ,  0.429924439903],
                          [ 0.5           ,  0.2           ,  0.429924439903],
                          [ 0.7           ,  0.2           ,  0.429924439903],
                          [ 0.9           ,  0.2           ,  0.429924439903],
                          [ 0.1           ,  0.4           ,  0.429924439903],
                          [ 0.3           ,  0.4           ,  0.429924439903],
                          [ 0.5           ,  0.4           ,  0.429924439903],
                          [ 0.7           ,  0.4           ,  0.429924439903],
                          [ 0.9           ,  0.4           ,  0.429924439903],
                          [ 0.1           ,  0.6           ,  0.429924439903],
                          [ 0.3           ,  0.6           ,  0.429924439903],
                          [ 0.5           ,  0.6           ,  0.429924439903],
                          [ 0.7           ,  0.6           ,  0.429924439903],
                          [ 0.9           ,  0.6           ,  0.429924439903],
                          [ 0.1           ,  0.8           ,  0.429924439903],
                          [ 0.3           ,  0.8           ,  0.429924439903],
                          [ 0.5           ,  0.8           ,  0.429924439903],
                          [ 0.7           ,  0.8           ,  0.429924439903],
                          [ 0.9           ,  0.8           ,  0.429924439903],
                          [ 0.1           ,  0.1           ,  0.440410401852],
                          [ 0.3           ,  0.1           ,  0.440410401852],
                          [ 0.5           ,  0.1           ,  0.440410401852],
                          [ 0.7           ,  0.1           ,  0.440410401852],
                          [ 0.9           ,  0.1           ,  0.440410401852],
                          [ 0.1           ,  0.3           ,  0.440410401852],
                          [ 0.3           ,  0.3           ,  0.440410401852],
                          [ 0.5           ,  0.3           ,  0.440410401852],
                          [ 0.7           ,  0.3           ,  0.440410401852],
                          [ 0.9           ,  0.3           ,  0.440410401852],
                          [ 0.1           ,  0.5           ,  0.440410401852],
                          [ 0.3           ,  0.5           ,  0.440410401852],
                          [ 0.5           ,  0.5           ,  0.440410401852],
                          [ 0.7           ,  0.5           ,  0.440410401852],
                          [ 0.9           ,  0.5           ,  0.440410401852],
                          [ 0.1           ,  0.7           ,  0.440410401852],
                          [ 0.3           ,  0.7           ,  0.440410401852],
                          [ 0.5           ,  0.7           ,  0.440410401852],
                          [ 0.7           ,  0.7           ,  0.440410401852],
                          [ 0.9           ,  0.7           ,  0.440410401852],
                          [ 0.1           ,  0.9           ,  0.440410401852],
                          [ 0.3           ,  0.9           ,  0.440410401852],
                          [ 0.5           ,  0.9           ,  0.440410401852],
                          [ 0.7           ,  0.9           ,  0.440410401852],
                          [ 0.9           ,  0.9           ,  0.440410401852],
                          [ 0.            ,  0.1           ,  0.450896363801],
                          [ 0.2           ,  0.1           ,  0.450896363801],
                          [ 0.4           ,  0.1           ,  0.450896363801],
                          [ 0.6           ,  0.1           ,  0.450896363801],
                          [ 0.8           ,  0.1           ,  0.450896363801],
                          [ 0.            ,  0.3           ,  0.450896363801],
                          [ 0.2           ,  0.3           ,  0.450896363801],
                          [ 0.4           ,  0.3           ,  0.450896363801],
                          [ 0.6           ,  0.3           ,  0.450896363801],
                          [ 0.8           ,  0.3           ,  0.450896363801],
                          [ 0.            ,  0.5           ,  0.450896363801],
                          [ 0.2           ,  0.5           ,  0.450896363801],
                          [ 0.4           ,  0.5           ,  0.450896363801],
                          [ 0.6           ,  0.5           ,  0.450896363801],
                          [ 0.8           ,  0.5           ,  0.450896363801],
                          [ 0.            ,  0.7           ,  0.450896363801],
                          [ 0.2           ,  0.7           ,  0.450896363801],
                          [ 0.4           ,  0.7           ,  0.450896363801],
                          [ 0.6           ,  0.7           ,  0.450896363801],
                          [ 0.8           ,  0.7           ,  0.450896363801],
                          [ 0.            ,  0.9           ,  0.450896363801],
                          [ 0.2           ,  0.9           ,  0.450896363801],
                          [ 0.4           ,  0.9           ,  0.450896363801],
                          [ 0.6           ,  0.9           ,  0.450896363801],
                          [ 0.8           ,  0.9           ,  0.450896363801],
                          [ 0.            ,  0.            ,  0.46138232575 ],
                          [ 0.2           ,  0.            ,  0.46138232575 ],
                          [ 0.4           ,  0.            ,  0.46138232575 ],
                          [ 0.6           ,  0.            ,  0.46138232575 ],
                          [ 0.8           ,  0.            ,  0.46138232575 ],
                          [ 0.            ,  0.2           ,  0.46138232575 ],
                          [ 0.2           ,  0.2           ,  0.46138232575 ],
                          [ 0.4           ,  0.2           ,  0.46138232575 ],
                          [ 0.6           ,  0.2           ,  0.46138232575 ],
                          [ 0.8           ,  0.2           ,  0.46138232575 ],
                          [ 0.            ,  0.4           ,  0.46138232575 ],
                          [ 0.2           ,  0.4           ,  0.46138232575 ],
                          [ 0.4           ,  0.4           ,  0.46138232575 ],
                          [ 0.6           ,  0.4           ,  0.46138232575 ],
                          [ 0.8           ,  0.4           ,  0.46138232575 ],
                          [ 0.            ,  0.6           ,  0.46138232575 ],
                          [ 0.2           ,  0.6           ,  0.46138232575 ],
                          [ 0.4           ,  0.6           ,  0.46138232575 ],
                          [ 0.6           ,  0.6           ,  0.46138232575 ],
                          [ 0.8           ,  0.6           ,  0.46138232575 ],
                          [ 0.            ,  0.8           ,  0.46138232575 ],
                          [ 0.2           ,  0.8           ,  0.46138232575 ],
                          [ 0.4           ,  0.8           ,  0.46138232575 ],
                          [ 0.6           ,  0.8           ,  0.46138232575 ],
                          [ 0.8           ,  0.8           ,  0.46138232575 ],
                          [ 0.1           ,  0.            ,  0.471868287699],
                          [ 0.3           ,  0.            ,  0.471868287699],
                          [ 0.5           ,  0.            ,  0.471868287699],
                          [ 0.7           ,  0.            ,  0.471868287699],
                          [ 0.9           ,  0.            ,  0.471868287699],
                          [ 0.1           ,  0.2           ,  0.471868287699],
                          [ 0.3           ,  0.2           ,  0.471868287699],
                          [ 0.5           ,  0.2           ,  0.471868287699],
                          [ 0.7           ,  0.2           ,  0.471868287699],
                          [ 0.9           ,  0.2           ,  0.471868287699],
                          [ 0.1           ,  0.4           ,  0.471868287699],
                          [ 0.3           ,  0.4           ,  0.471868287699],
                          [ 0.5           ,  0.4           ,  0.471868287699],
                          [ 0.7           ,  0.4           ,  0.471868287699],
                          [ 0.9           ,  0.4           ,  0.471868287699],
                          [ 0.1           ,  0.6           ,  0.471868287699],
                          [ 0.3           ,  0.6           ,  0.471868287699],
                          [ 0.5           ,  0.6           ,  0.471868287699],
                          [ 0.7           ,  0.6           ,  0.471868287699],
                          [ 0.9           ,  0.6           ,  0.471868287699],
                          [ 0.1           ,  0.8           ,  0.471868287699],
                          [ 0.3           ,  0.8           ,  0.471868287699],
                          [ 0.5           ,  0.8           ,  0.471868287699],
                          [ 0.7           ,  0.8           ,  0.471868287699],
                          [ 0.9           ,  0.8           ,  0.471868287699],
                          [ 0.1           ,  0.1           ,  0.482354249648],
                          [ 0.3           ,  0.1           ,  0.482354249648],
                          [ 0.5           ,  0.1           ,  0.482354249648],
                          [ 0.7           ,  0.1           ,  0.482354249648],
                          [ 0.9           ,  0.1           ,  0.482354249648],
                          [ 0.1           ,  0.3           ,  0.482354249648],
                          [ 0.3           ,  0.3           ,  0.482354249648],
                          [ 0.5           ,  0.3           ,  0.482354249648],
                          [ 0.7           ,  0.3           ,  0.482354249648],
                          [ 0.9           ,  0.3           ,  0.482354249648],
                          [ 0.1           ,  0.5           ,  0.482354249648],
                          [ 0.3           ,  0.5           ,  0.482354249648],
                          [ 0.5           ,  0.5           ,  0.482354249648],
                          [ 0.7           ,  0.5           ,  0.482354249648],
                          [ 0.9           ,  0.5           ,  0.482354249648],
                          [ 0.1           ,  0.7           ,  0.482354249648],
                          [ 0.3           ,  0.7           ,  0.482354249648],
                          [ 0.5           ,  0.7           ,  0.482354249648],
                          [ 0.7           ,  0.7           ,  0.482354249648],
                          [ 0.9           ,  0.7           ,  0.482354249648],
                          [ 0.1           ,  0.9           ,  0.482354249648],
                          [ 0.3           ,  0.9           ,  0.482354249648],
                          [ 0.5           ,  0.9           ,  0.482354249648],
                          [ 0.7           ,  0.9           ,  0.482354249648],
                          [ 0.9           ,  0.9           ,  0.482354249648],
                          [ 0.            ,  0.1           ,  0.492840211597],
                          [ 0.2           ,  0.1           ,  0.492840211597],
                          [ 0.4           ,  0.1           ,  0.492840211597],
                          [ 0.6           ,  0.1           ,  0.492840211597],
                          [ 0.8           ,  0.1           ,  0.492840211597],
                          [ 0.            ,  0.3           ,  0.492840211597],
                          [ 0.2           ,  0.3           ,  0.492840211597],
                          [ 0.4           ,  0.3           ,  0.492840211597],
                          [ 0.6           ,  0.3           ,  0.492840211597],
                          [ 0.8           ,  0.3           ,  0.492840211597],
                          [ 0.            ,  0.5           ,  0.492840211597],
                          [ 0.2           ,  0.5           ,  0.492840211597],
                          [ 0.4           ,  0.5           ,  0.492840211597],
                          [ 0.6           ,  0.5           ,  0.492840211597],
                          [ 0.8           ,  0.5           ,  0.492840211597],
                          [ 0.            ,  0.7           ,  0.492840211597],
                          [ 0.2           ,  0.7           ,  0.492840211597],
                          [ 0.4           ,  0.7           ,  0.492840211597],
                          [ 0.6           ,  0.7           ,  0.492840211597],
                          [ 0.8           ,  0.7           ,  0.492840211597],
                          [ 0.            ,  0.9           ,  0.492840211597],
                          [ 0.2           ,  0.9           ,  0.492840211597],
                          [ 0.4           ,  0.9           ,  0.492840211597],
                          [ 0.6           ,  0.9           ,  0.492840211597],
                          [ 0.8           ,  0.9           ,  0.492840211597],
                          [ 0.            ,  0.            ,  0.503326173545],
                          [ 0.2           ,  0.            ,  0.503326173545],
                          [ 0.4           ,  0.            ,  0.503326173545],
                          [ 0.6           ,  0.            ,  0.503326173545],
                          [ 0.8           ,  0.            ,  0.503326173545],
                          [ 0.            ,  0.2           ,  0.503326173545],
                          [ 0.2           ,  0.2           ,  0.503326173545],
                          [ 0.4           ,  0.2           ,  0.503326173545],
                          [ 0.6           ,  0.2           ,  0.503326173545],
                          [ 0.8           ,  0.2           ,  0.503326173545],
                          [ 0.            ,  0.4           ,  0.503326173545],
                          [ 0.2           ,  0.4           ,  0.503326173545],
                          [ 0.4           ,  0.4           ,  0.503326173545],
                          [ 0.6           ,  0.4           ,  0.503326173545],
                          [ 0.8           ,  0.4           ,  0.503326173545],
                          [ 0.            ,  0.6           ,  0.503326173545],
                          [ 0.2           ,  0.6           ,  0.503326173545],
                          [ 0.4           ,  0.6           ,  0.503326173545],
                          [ 0.6           ,  0.6           ,  0.503326173545],
                          [ 0.8           ,  0.6           ,  0.503326173545],
                          [ 0.            ,  0.8           ,  0.503326173545],
                          [ 0.2           ,  0.8           ,  0.503326173545],
                          [ 0.4           ,  0.8           ,  0.503326173545],
                          [ 0.6           ,  0.8           ,  0.503326173545],
                          [ 0.8           ,  0.8           ,  0.503326173545],
                          [ 0.1           ,  0.            ,  0.513812135494],
                          [ 0.3           ,  0.            ,  0.513812135494],
                          [ 0.5           ,  0.            ,  0.513812135494],
                          [ 0.7           ,  0.            ,  0.513812135494],
                          [ 0.9           ,  0.            ,  0.513812135494],
                          [ 0.1           ,  0.2           ,  0.513812135494],
                          [ 0.3           ,  0.2           ,  0.513812135494],
                          [ 0.5           ,  0.2           ,  0.513812135494],
                          [ 0.7           ,  0.2           ,  0.513812135494],
                          [ 0.9           ,  0.2           ,  0.513812135494],
                          [ 0.1           ,  0.4           ,  0.513812135494],
                          [ 0.3           ,  0.4           ,  0.513812135494],
                          [ 0.5           ,  0.4           ,  0.513812135494],
                          [ 0.7           ,  0.4           ,  0.513812135494],
                          [ 0.9           ,  0.4           ,  0.513812135494],
                          [ 0.1           ,  0.6           ,  0.513812135494],
                          [ 0.3           ,  0.6           ,  0.513812135494],
                          [ 0.5           ,  0.6           ,  0.513812135494],
                          [ 0.7           ,  0.6           ,  0.513812135494],
                          [ 0.9           ,  0.6           ,  0.513812135494],
                          [ 0.1           ,  0.8           ,  0.513812135494],
                          [ 0.3           ,  0.8           ,  0.513812135494],
                          [ 0.5           ,  0.8           ,  0.513812135494],
                          [ 0.7           ,  0.8           ,  0.513812135494],
                          [ 0.9           ,  0.8           ,  0.513812135494],
                          [ 0.1           ,  0.1           ,  0.524298097443],
                          [ 0.3           ,  0.1           ,  0.524298097443],
                          [ 0.5           ,  0.1           ,  0.524298097443],
                          [ 0.7           ,  0.1           ,  0.524298097443],
                          [ 0.9           ,  0.1           ,  0.524298097443],
                          [ 0.1           ,  0.3           ,  0.524298097443],
                          [ 0.3           ,  0.3           ,  0.524298097443],
                          [ 0.5           ,  0.3           ,  0.524298097443],
                          [ 0.7           ,  0.3           ,  0.524298097443],
                          [ 0.9           ,  0.3           ,  0.524298097443],
                          [ 0.1           ,  0.5           ,  0.524298097443],
                          [ 0.3           ,  0.5           ,  0.524298097443],
                          [ 0.5           ,  0.5           ,  0.524298097443],
                          [ 0.7           ,  0.5           ,  0.524298097443],
                          [ 0.9           ,  0.5           ,  0.524298097443],
                          [ 0.1           ,  0.7           ,  0.524298097443],
                          [ 0.3           ,  0.7           ,  0.524298097443],
                          [ 0.5           ,  0.7           ,  0.524298097443],
                          [ 0.7           ,  0.7           ,  0.524298097443],
                          [ 0.9           ,  0.7           ,  0.524298097443],
                          [ 0.1           ,  0.9           ,  0.524298097443],
                          [ 0.3           ,  0.9           ,  0.524298097443],
                          [ 0.5           ,  0.9           ,  0.524298097443],
                          [ 0.7           ,  0.9           ,  0.524298097443],
                          [ 0.9           ,  0.9           ,  0.524298097443],
                          [ 0.            ,  0.1           ,  0.534784059392],
                          [ 0.2           ,  0.1           ,  0.534784059392],
                          [ 0.4           ,  0.1           ,  0.534784059392],
                          [ 0.6           ,  0.1           ,  0.534784059392],
                          [ 0.8           ,  0.1           ,  0.534784059392],
                          [ 0.            ,  0.3           ,  0.534784059392],
                          [ 0.2           ,  0.3           ,  0.534784059392],
                          [ 0.4           ,  0.3           ,  0.534784059392],
                          [ 0.6           ,  0.3           ,  0.534784059392],
                          [ 0.8           ,  0.3           ,  0.534784059392],
                          [ 0.            ,  0.5           ,  0.534784059392],
                          [ 0.2           ,  0.5           ,  0.534784059392],
                          [ 0.4           ,  0.5           ,  0.534784059392],
                          [ 0.6           ,  0.5           ,  0.534784059392],
                          [ 0.8           ,  0.5           ,  0.534784059392],
                          [ 0.            ,  0.7           ,  0.534784059392],
                          [ 0.2           ,  0.7           ,  0.534784059392],
                          [ 0.4           ,  0.7           ,  0.534784059392],
                          [ 0.6           ,  0.7           ,  0.534784059392],
                          [ 0.8           ,  0.7           ,  0.534784059392],
                          [ 0.            ,  0.9           ,  0.534784059392],
                          [ 0.2           ,  0.9           ,  0.534784059392],
                          [ 0.4           ,  0.9           ,  0.534784059392],
                          [ 0.6           ,  0.9           ,  0.534784059392],
                          [ 0.8           ,  0.9           ,  0.534784059392],
                          [ 0.            ,  0.            ,  0.545270021341],
                          [ 0.2           ,  0.            ,  0.545270021341],
                          [ 0.4           ,  0.            ,  0.545270021341],
                          [ 0.6           ,  0.            ,  0.545270021341],
                          [ 0.8           ,  0.            ,  0.545270021341],
                          [ 0.            ,  0.2           ,  0.545270021341],
                          [ 0.2           ,  0.2           ,  0.545270021341],
                          [ 0.4           ,  0.2           ,  0.545270021341],
                          [ 0.6           ,  0.2           ,  0.545270021341],
                          [ 0.8           ,  0.2           ,  0.545270021341],
                          [ 0.            ,  0.4           ,  0.545270021341],
                          [ 0.2           ,  0.4           ,  0.545270021341],
                          [ 0.4           ,  0.4           ,  0.545270021341],
                          [ 0.6           ,  0.4           ,  0.545270021341],
                          [ 0.8           ,  0.4           ,  0.545270021341],
                          [ 0.            ,  0.6           ,  0.545270021341],
                          [ 0.2           ,  0.6           ,  0.545270021341],
                          [ 0.4           ,  0.6           ,  0.545270021341],
                          [ 0.6           ,  0.6           ,  0.545270021341],
                          [ 0.8           ,  0.6           ,  0.545270021341],
                          [ 0.            ,  0.8           ,  0.545270021341],
                          [ 0.2           ,  0.8           ,  0.545270021341],
                          [ 0.4           ,  0.8           ,  0.545270021341],
                          [ 0.6           ,  0.8           ,  0.545270021341],
                          [ 0.8           ,  0.8           ,  0.545270021341],
                          [ 0.1           ,  0.            ,  0.55575598329 ],
                          [ 0.3           ,  0.            ,  0.55575598329 ],
                          [ 0.5           ,  0.            ,  0.55575598329 ],
                          [ 0.7           ,  0.            ,  0.55575598329 ],
                          [ 0.9           ,  0.            ,  0.55575598329 ],
                          [ 0.1           ,  0.2           ,  0.55575598329 ],
                          [ 0.3           ,  0.2           ,  0.55575598329 ],
                          [ 0.5           ,  0.2           ,  0.55575598329 ],
                          [ 0.7           ,  0.2           ,  0.55575598329 ],
                          [ 0.9           ,  0.2           ,  0.55575598329 ],
                          [ 0.1           ,  0.4           ,  0.55575598329 ],
                          [ 0.3           ,  0.4           ,  0.55575598329 ],
                          [ 0.5           ,  0.4           ,  0.55575598329 ],
                          [ 0.7           ,  0.4           ,  0.55575598329 ],
                          [ 0.9           ,  0.4           ,  0.55575598329 ],
                          [ 0.1           ,  0.6           ,  0.55575598329 ],
                          [ 0.3           ,  0.6           ,  0.55575598329 ],
                          [ 0.5           ,  0.6           ,  0.55575598329 ],
                          [ 0.7           ,  0.6           ,  0.55575598329 ],
                          [ 0.9           ,  0.6           ,  0.55575598329 ],
                          [ 0.1           ,  0.8           ,  0.55575598329 ],
                          [ 0.3           ,  0.8           ,  0.55575598329 ],
                          [ 0.5           ,  0.8           ,  0.55575598329 ],
                          [ 0.7           ,  0.8           ,  0.55575598329 ],
                          [ 0.9           ,  0.8           ,  0.55575598329 ],
                          [ 0.1           ,  0.1           ,  0.566241945238],
                          [ 0.3           ,  0.1           ,  0.566241945238],
                          [ 0.5           ,  0.1           ,  0.566241945238],
                          [ 0.7           ,  0.1           ,  0.566241945238],
                          [ 0.9           ,  0.1           ,  0.566241945238],
                          [ 0.1           ,  0.3           ,  0.566241945238],
                          [ 0.3           ,  0.3           ,  0.566241945238],
                          [ 0.5           ,  0.3           ,  0.566241945238],
                          [ 0.7           ,  0.3           ,  0.566241945238],
                          [ 0.9           ,  0.3           ,  0.566241945238],
                          [ 0.1           ,  0.5           ,  0.566241945238],
                          [ 0.3           ,  0.5           ,  0.566241945238],
                          [ 0.5           ,  0.5           ,  0.566241945238],
                          [ 0.7           ,  0.5           ,  0.566241945238],
                          [ 0.9           ,  0.5           ,  0.566241945238],
                          [ 0.1           ,  0.7           ,  0.566241945238],
                          [ 0.3           ,  0.7           ,  0.566241945238],
                          [ 0.5           ,  0.7           ,  0.566241945238],
                          [ 0.7           ,  0.7           ,  0.566241945238],
                          [ 0.9           ,  0.7           ,  0.566241945238],
                          [ 0.1           ,  0.9           ,  0.566241945238],
                          [ 0.3           ,  0.9           ,  0.566241945238],
                          [ 0.5           ,  0.9           ,  0.566241945238],
                          [ 0.7           ,  0.9           ,  0.566241945238],
                          [ 0.9           ,  0.9           ,  0.566241945238],
                          [ 0.            ,  0.1           ,  0.576727907187],
                          [ 0.2           ,  0.1           ,  0.576727907187],
                          [ 0.4           ,  0.1           ,  0.576727907187],
                          [ 0.6           ,  0.1           ,  0.576727907187],
                          [ 0.8           ,  0.1           ,  0.576727907187],
                          [ 0.            ,  0.3           ,  0.576727907187],
                          [ 0.2           ,  0.3           ,  0.576727907187],
                          [ 0.4           ,  0.3           ,  0.576727907187],
                          [ 0.6           ,  0.3           ,  0.576727907187],
                          [ 0.8           ,  0.3           ,  0.576727907187],
                          [ 0.            ,  0.5           ,  0.576727907187],
                          [ 0.2           ,  0.5           ,  0.576727907187],
                          [ 0.4           ,  0.5           ,  0.576727907187],
                          [ 0.6           ,  0.5           ,  0.576727907187],
                          [ 0.8           ,  0.5           ,  0.576727907187],
                          [ 0.            ,  0.7           ,  0.576727907187],
                          [ 0.2           ,  0.7           ,  0.576727907187],
                          [ 0.4           ,  0.7           ,  0.576727907187],
                          [ 0.6           ,  0.7           ,  0.576727907187],
                          [ 0.8           ,  0.7           ,  0.576727907187],
                          [ 0.            ,  0.9           ,  0.576727907187],
                          [ 0.2           ,  0.9           ,  0.576727907187],
                          [ 0.4           ,  0.9           ,  0.576727907187],
                          [ 0.6           ,  0.9           ,  0.576727907187],
                          [ 0.8           ,  0.9           ,  0.576727907187],
                          [ 0.            ,  0.            ,  0.587213869136],
                          [ 0.2           ,  0.            ,  0.587213869136],
                          [ 0.4           ,  0.            ,  0.587213869136],
                          [ 0.6           ,  0.            ,  0.587213869136],
                          [ 0.8           ,  0.            ,  0.587213869136],
                          [ 0.            ,  0.2           ,  0.587213869136],
                          [ 0.2           ,  0.2           ,  0.587213869136],
                          [ 0.4           ,  0.2           ,  0.587213869136],
                          [ 0.6           ,  0.2           ,  0.587213869136],
                          [ 0.8           ,  0.2           ,  0.587213869136],
                          [ 0.            ,  0.4           ,  0.587213869136],
                          [ 0.2           ,  0.4           ,  0.587213869136],
                          [ 0.4           ,  0.4           ,  0.587213869136],
                          [ 0.6           ,  0.4           ,  0.587213869136],
                          [ 0.8           ,  0.4           ,  0.587213869136],
                          [ 0.            ,  0.6           ,  0.587213869136],
                          [ 0.2           ,  0.6           ,  0.587213869136],
                          [ 0.4           ,  0.6           ,  0.587213869136],
                          [ 0.6           ,  0.6           ,  0.587213869136],
                          [ 0.8           ,  0.6           ,  0.587213869136],
                          [ 0.            ,  0.8           ,  0.587213869136],
                          [ 0.2           ,  0.8           ,  0.587213869136],
                          [ 0.4           ,  0.8           ,  0.587213869136],
                          [ 0.6           ,  0.8           ,  0.587213869136],
                          [ 0.8           ,  0.8           ,  0.587213869136],
                          [ 0.1           ,  0.            ,  0.597699831085],
                          [ 0.3           ,  0.            ,  0.597699831085],
                          [ 0.5           ,  0.            ,  0.597699831085],
                          [ 0.7           ,  0.            ,  0.597699831085],
                          [ 0.9           ,  0.            ,  0.597699831085],
                          [ 0.1           ,  0.2           ,  0.597699831085],
                          [ 0.3           ,  0.2           ,  0.597699831085],
                          [ 0.5           ,  0.2           ,  0.597699831085],
                          [ 0.7           ,  0.2           ,  0.597699831085],
                          [ 0.9           ,  0.2           ,  0.597699831085],
                          [ 0.1           ,  0.4           ,  0.597699831085],
                          [ 0.3           ,  0.4           ,  0.597699831085],
                          [ 0.5           ,  0.4           ,  0.597699831085],
                          [ 0.7           ,  0.4           ,  0.597699831085],
                          [ 0.9           ,  0.4           ,  0.597699831085],
                          [ 0.1           ,  0.6           ,  0.597699831085],
                          [ 0.3           ,  0.6           ,  0.597699831085],
                          [ 0.5           ,  0.6           ,  0.597699831085],
                          [ 0.7           ,  0.6           ,  0.597699831085],
                          [ 0.9           ,  0.6           ,  0.597699831085],
                          [ 0.1           ,  0.8           ,  0.597699831085],
                          [ 0.3           ,  0.8           ,  0.597699831085],
                          [ 0.5           ,  0.8           ,  0.597699831085],
                          [ 0.7           ,  0.8           ,  0.597699831085],
                          [ 0.9           ,  0.8           ,  0.597699831085],
                          [ 0.1           ,  0.1           ,  0.608185793034],
                          [ 0.3           ,  0.1           ,  0.608185793034],
                          [ 0.5           ,  0.1           ,  0.608185793034],
                          [ 0.7           ,  0.1           ,  0.608185793034],
                          [ 0.9           ,  0.1           ,  0.608185793034],
                          [ 0.1           ,  0.3           ,  0.608185793034],
                          [ 0.3           ,  0.3           ,  0.608185793034],
                          [ 0.5           ,  0.3           ,  0.608185793034],
                          [ 0.7           ,  0.3           ,  0.608185793034],
                          [ 0.9           ,  0.3           ,  0.608185793034],
                          [ 0.1           ,  0.5           ,  0.608185793034],
                          [ 0.3           ,  0.5           ,  0.608185793034],
                          [ 0.5           ,  0.5           ,  0.608185793034],
                          [ 0.7           ,  0.5           ,  0.608185793034],
                          [ 0.9           ,  0.5           ,  0.608185793034],
                          [ 0.1           ,  0.7           ,  0.608185793034],
                          [ 0.3           ,  0.7           ,  0.608185793034],
                          [ 0.5           ,  0.7           ,  0.608185793034],
                          [ 0.7           ,  0.7           ,  0.608185793034],
                          [ 0.9           ,  0.7           ,  0.608185793034],
                          [ 0.1           ,  0.9           ,  0.608185793034],
                          [ 0.3           ,  0.9           ,  0.608185793034],
                          [ 0.5           ,  0.9           ,  0.608185793034],
                          [ 0.7           ,  0.9           ,  0.608185793034],
                          [ 0.9           ,  0.9           ,  0.608185793034],
                          [ 0.            ,  0.1           ,  0.618671754983],
                          [ 0.2           ,  0.1           ,  0.618671754983],
                          [ 0.4           ,  0.1           ,  0.618671754983],
                          [ 0.6           ,  0.1           ,  0.618671754983],
                          [ 0.8           ,  0.1           ,  0.618671754983],
                          [ 0.            ,  0.3           ,  0.618671754983],
                          [ 0.2           ,  0.3           ,  0.618671754983],
                          [ 0.4           ,  0.3           ,  0.618671754983],
                          [ 0.6           ,  0.3           ,  0.618671754983],
                          [ 0.8           ,  0.3           ,  0.618671754983],
                          [ 0.            ,  0.5           ,  0.618671754983],
                          [ 0.2           ,  0.5           ,  0.618671754983],
                          [ 0.4           ,  0.5           ,  0.618671754983],
                          [ 0.6           ,  0.5           ,  0.618671754983],
                          [ 0.8           ,  0.5           ,  0.618671754983],
                          [ 0.            ,  0.7           ,  0.618671754983],
                          [ 0.2           ,  0.7           ,  0.618671754983],
                          [ 0.4           ,  0.7           ,  0.618671754983],
                          [ 0.6           ,  0.7           ,  0.618671754983],
                          [ 0.8           ,  0.7           ,  0.618671754983],
                          [ 0.            ,  0.9           ,  0.618671754983],
                          [ 0.2           ,  0.9           ,  0.618671754983],
                          [ 0.4           ,  0.9           ,  0.618671754983],
                          [ 0.6           ,  0.9           ,  0.618671754983],
                          [ 0.8           ,  0.9           ,  0.618671754983],
                          [ 0.            ,  0.            ,  0.629157716932],
                          [ 0.2           ,  0.            ,  0.629157716932],
                          [ 0.4           ,  0.            ,  0.629157716932],
                          [ 0.6           ,  0.            ,  0.629157716932],
                          [ 0.8           ,  0.            ,  0.629157716932],
                          [ 0.            ,  0.2           ,  0.629157716932],
                          [ 0.2           ,  0.2           ,  0.629157716932],
                          [ 0.4           ,  0.2           ,  0.629157716932],
                          [ 0.6           ,  0.2           ,  0.629157716932],
                          [ 0.8           ,  0.2           ,  0.629157716932],
                          [ 0.            ,  0.4           ,  0.629157716932],
                          [ 0.2           ,  0.4           ,  0.629157716932],
                          [ 0.4           ,  0.4           ,  0.629157716932],
                          [ 0.6           ,  0.4           ,  0.629157716932],
                          [ 0.8           ,  0.4           ,  0.629157716932],
                          [ 0.            ,  0.6           ,  0.629157716932],
                          [ 0.2           ,  0.6           ,  0.629157716932],
                          [ 0.4           ,  0.6           ,  0.629157716932],
                          [ 0.6           ,  0.6           ,  0.629157716932],
                          [ 0.8           ,  0.6           ,  0.629157716932],
                          [ 0.            ,  0.8           ,  0.629157716932],
                          [ 0.2           ,  0.8           ,  0.629157716932],
                          [ 0.4           ,  0.8           ,  0.629157716932],
                          [ 0.6           ,  0.8           ,  0.629157716932],
                          [ 0.8           ,  0.8           ,  0.629157716932],
                          [ 0.1           ,  0.            ,  0.63964367888 ],
                          [ 0.3           ,  0.            ,  0.63964367888 ],
                          [ 0.5           ,  0.            ,  0.63964367888 ],
                          [ 0.7           ,  0.            ,  0.63964367888 ],
                          [ 0.9           ,  0.            ,  0.63964367888 ],
                          [ 0.1           ,  0.2           ,  0.63964367888 ],
                          [ 0.3           ,  0.2           ,  0.63964367888 ],
                          [ 0.5           ,  0.2           ,  0.63964367888 ],
                          [ 0.7           ,  0.2           ,  0.63964367888 ],
                          [ 0.9           ,  0.2           ,  0.63964367888 ],
                          [ 0.1           ,  0.4           ,  0.63964367888 ],
                          [ 0.3           ,  0.4           ,  0.63964367888 ],
                          [ 0.5           ,  0.4           ,  0.63964367888 ],
                          [ 0.7           ,  0.4           ,  0.63964367888 ],
                          [ 0.9           ,  0.4           ,  0.63964367888 ],
                          [ 0.1           ,  0.6           ,  0.63964367888 ],
                          [ 0.3           ,  0.6           ,  0.63964367888 ],
                          [ 0.5           ,  0.6           ,  0.63964367888 ],
                          [ 0.7           ,  0.6           ,  0.63964367888 ],
                          [ 0.9           ,  0.6           ,  0.63964367888 ],
                          [ 0.1           ,  0.8           ,  0.63964367888 ],
                          [ 0.3           ,  0.8           ,  0.63964367888 ],
                          [ 0.5           ,  0.8           ,  0.63964367888 ],
                          [ 0.7           ,  0.8           ,  0.63964367888 ],
                          [ 0.9           ,  0.8           ,  0.63964367888 ],
                          [ 0.1           ,  0.1           ,  0.650129640829],
                          [ 0.3           ,  0.1           ,  0.650129640829],
                          [ 0.5           ,  0.1           ,  0.650129640829],
                          [ 0.7           ,  0.1           ,  0.650129640829],
                          [ 0.9           ,  0.1           ,  0.650129640829],
                          [ 0.1           ,  0.3           ,  0.650129640829],
                          [ 0.3           ,  0.3           ,  0.650129640829],
                          [ 0.5           ,  0.3           ,  0.650129640829],
                          [ 0.7           ,  0.3           ,  0.650129640829],
                          [ 0.9           ,  0.3           ,  0.650129640829],
                          [ 0.1           ,  0.5           ,  0.650129640829],
                          [ 0.3           ,  0.5           ,  0.650129640829],
                          [ 0.5           ,  0.5           ,  0.650129640829],
                          [ 0.7           ,  0.5           ,  0.650129640829],
                          [ 0.9           ,  0.5           ,  0.650129640829],
                          [ 0.1           ,  0.7           ,  0.650129640829],
                          [ 0.3           ,  0.7           ,  0.650129640829],
                          [ 0.5           ,  0.7           ,  0.650129640829],
                          [ 0.7           ,  0.7           ,  0.650129640829],
                          [ 0.9           ,  0.7           ,  0.650129640829],
                          [ 0.1           ,  0.9           ,  0.650129640829],
                          [ 0.3           ,  0.9           ,  0.650129640829],
                          [ 0.5           ,  0.9           ,  0.650129640829],
                          [ 0.7           ,  0.9           ,  0.650129640829],
                          [ 0.9           ,  0.9           ,  0.650129640829],
                          [ 0.            ,  0.1           ,  0.660615602778],
                          [ 0.2           ,  0.1           ,  0.660615602778],
                          [ 0.4           ,  0.1           ,  0.660615602778],
                          [ 0.6           ,  0.1           ,  0.660615602778],
                          [ 0.8           ,  0.1           ,  0.660615602778],
                          [ 0.            ,  0.3           ,  0.660615602778],
                          [ 0.2           ,  0.3           ,  0.660615602778],
                          [ 0.4           ,  0.3           ,  0.660615602778],
                          [ 0.6           ,  0.3           ,  0.660615602778],
                          [ 0.8           ,  0.3           ,  0.660615602778],
                          [ 0.            ,  0.5           ,  0.660615602778],
                          [ 0.2           ,  0.5           ,  0.660615602778],
                          [ 0.4           ,  0.5           ,  0.660615602778],
                          [ 0.6           ,  0.5           ,  0.660615602778],
                          [ 0.8           ,  0.5           ,  0.660615602778],
                          [ 0.            ,  0.7           ,  0.660615602778],
                          [ 0.2           ,  0.7           ,  0.660615602778],
                          [ 0.4           ,  0.7           ,  0.660615602778],
                          [ 0.6           ,  0.7           ,  0.660615602778],
                          [ 0.8           ,  0.7           ,  0.660615602778],
                          [ 0.            ,  0.9           ,  0.660615602778],
                          [ 0.2           ,  0.9           ,  0.660615602778],
                          [ 0.4           ,  0.9           ,  0.660615602778],
                          [ 0.6           ,  0.9           ,  0.660615602778],
                          [ 0.8           ,  0.9           ,  0.660615602778],
                          [ 0.            ,  0.            ,  0.671101564727],
                          [ 0.2           ,  0.            ,  0.671101564727],
                          [ 0.4           ,  0.            ,  0.671101564727],
                          [ 0.6           ,  0.            ,  0.671101564727],
                          [ 0.8           ,  0.            ,  0.671101564727],
                          [ 0.            ,  0.2           ,  0.671101564727],
                          [ 0.2           ,  0.2           ,  0.671101564727],
                          [ 0.4           ,  0.2           ,  0.671101564727],
                          [ 0.6           ,  0.2           ,  0.671101564727],
                          [ 0.8           ,  0.2           ,  0.671101564727],
                          [ 0.            ,  0.4           ,  0.671101564727],
                          [ 0.2           ,  0.4           ,  0.671101564727],
                          [ 0.4           ,  0.4           ,  0.671101564727],
                          [ 0.6           ,  0.4           ,  0.671101564727],
                          [ 0.8           ,  0.4           ,  0.671101564727],
                          [ 0.            ,  0.6           ,  0.671101564727],
                          [ 0.2           ,  0.6           ,  0.671101564727],
                          [ 0.4           ,  0.6           ,  0.671101564727],
                          [ 0.6           ,  0.6           ,  0.671101564727],
                          [ 0.8           ,  0.6           ,  0.671101564727],
                          [ 0.            ,  0.8           ,  0.671101564727],
                          [ 0.2           ,  0.8           ,  0.671101564727],
                          [ 0.4           ,  0.8           ,  0.671101564727],
                          [ 0.6           ,  0.8           ,  0.671101564727],
                          [ 0.8           ,  0.8           ,  0.671101564727]]

# Set up configuration
si_long = BulkConfiguration(
    bravais_lattice=lattice,
    elements=elements,
    fractional_coordinates=fractional_coordinates
    )

# Add tags
si_long.addTags('apply_heat',       [1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057,
                                     1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065,
                                     1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073,
                                     1074, 1075, 1076, 1077, 1078, 1079, 1080, 1081,
                                     1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089,
                                     1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097,
                                     1098, 1099, 1100, 1101, 1102, 1103, 1104, 1105,
                                     1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113,
                                     1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121,
                                     1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129,
                                     1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137,
                                     1138, 1139, 1140, 1141, 1142, 1143, 1144, 1145,
                                     1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153,
                                     1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161,
                                     1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169,
                                     1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177,
                                     1178, 1179, 1180, 1181, 1182, 1183, 1184, 1185,
                                     1186, 1187, 1188, 1189, 1190, 1191, 1192, 1193,
                                     1194, 1195, 1196, 1197, 1198, 1199, 1200, 1201,
                                     1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209,
                                     1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217,
                                     1218, 1219, 1220, 1221, 1222, 1223, 1224, 1225,
                                     1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233,
                                     1234, 1235, 1236, 1237, 1238, 1239, 1240, 1241,
                                     1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249,
                                     1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257,
                                     1258, 1259, 1260, 1261, 1262, 1263, 1264, 1265,
                                     1266, 1267, 1268, 1269, 1270, 1271, 1272, 1273,
                                     1274, 1275, 1276, 1277, 1278, 1279, 1280, 1281,
                                     1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289,
                                     1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297,
                                     1298, 1299, 1300, 1301, 1302, 1303, 1304, 1305,
                                     1306, 1307, 1308, 1309, 1310, 1311, 1312, 1313,
                                     1314, 1315, 1316, 1317, 1318, 1319, 1320, 1321,
                                     1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329,
                                     1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337,
                                     1338, 1339, 1340, 1341, 1342, 1343, 1344, 1345,
                                     1346, 1347, 1348, 1349, 1350, 1351, 1352, 1353,
                                     1354, 1355, 1356, 1357, 1358, 1359, 1360, 1361,
                                     1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369,
                                     1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377,
                                     1378, 1379, 1380, 1381, 1382, 1383, 1384, 1385,
                                     1386, 1387, 1388, 1389, 1390, 1391, 1392, 1393,
                                     1394, 1395, 1396, 1397, 1398, 1399, 1400, 1401,
                                     1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409,
                                     1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417,
                                     1418, 1419, 1420, 1421, 1422, 1423, 1424, 1425,
                                     1426, 1427, 1428, 1429, 1430, 1431, 1432, 1433,
                                     1434, 1435, 1436, 1437, 1438, 1439, 1440, 1441,
                                     1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449,
                                     1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457,
                                     1458, 1459, 1460, 1461, 1462, 1463, 1464, 1465,
                                     1466, 1467, 1468, 1469, 1470, 1471, 1472, 1473,
                                     1474, 1475, 1476, 1477, 1478, 1479, 1480, 1481,
                                     1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489,
                                     1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497,
                                     1498, 1499, 1500, 1501, 1502, 1503, 1504, 1505,
                                     1506, 1507, 1508, 1509, 1510, 1511, 1512, 1513,
                                     1514, 1515, 1516, 1517, 1518, 1519, 1520, 1521,
                                     1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529,
                                     1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537,
                                     1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545,
                                     1546, 1547, 1548, 1549, 1550, 1551, 1552, 1553,
                                     1554, 1555, 1556, 1557, 1558, 1559, 1560, 1561,
                                     1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569,
                                     1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577,
                                     1578, 1579, 1580, 1581, 1582, 1583, 1584, 1585,
                                     1586, 1587, 1588, 1589, 1590, 1591, 1592, 1593,
                                     1594, 1595, 1596, 1597, 1598, 1599])
si_long.addTags('fixed_layer',      [  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
                                      10,  11,  12,  13,  14,  15,  16,  17,  18,  19,
                                      20,  21,  22,  23,  24,  25,  26,  27,  28,  29,
                                      30,  31,  32,  33,  34,  35,  36,  37,  38,  39,
                                      40,  41,  42,  43,  44,  45,  46,  47,  48,  49,
                                      50,  51,  52,  53,  54,  55,  56,  57,  58,  59,
                                      60,  61,  62,  63,  64,  65,  66,  67,  68,  69,
                                      70,  71,  72,  73,  74,  75,  76,  77,  78,  79,
                                      80,  81,  82,  83,  84,  85,  86,  87,  88,  89,
                                      90,  91,  92,  93,  94,  95,  96,  97,  98,  99,
                                     100, 101, 102, 103, 104, 105, 106, 107, 108, 109,
                                     110, 111, 112, 113, 114, 115, 116, 117, 118, 119,
                                     120, 121, 122, 123, 124])
si_long.addTags('thermostat_layer', [ 125,  126,  127,  128,  129,  130,  131,  132,
                                      133,  134,  135,  136,  137,  138,  139,  140,
                                      141,  142,  143,  144,  145,  146,  147,  148,
                                      149,  150,  151,  152,  153,  154,  155,  156,
                                      157,  158,  159,  160,  161,  162,  163,  164,
                                      165,  166,  167,  168,  169,  170,  171,  172,
                                      173,  174,  175,  176,  177,  178,  179,  180,
                                      181,  182,  183,  184,  185,  186,  187,  188,
                                      189,  190,  191,  192,  193,  194,  195,  196,
                                      197,  198,  199,  200,  201,  202,  203,  204,
                                      205,  206,  207,  208,  209,  210,  211,  212,
                                      213,  214,  215,  216,  217,  218,  219,  220,
                                      221,  222,  223,  224,  225,  226,  227,  228,
                                      229,  230,  231,  232,  233,  234,  235,  236,
                                      237,  238,  239,  240,  241,  242,  243,  244,
                                      245,  246,  247,  248,  249,  250,  251,  252,
                                      253,  254,  255,  256,  257,  258,  259,  260,
                                      261,  262,  263,  264,  265,  266,  267,  268,
                                      269,  270,  271,  272,  273,  274,  275,  276,
                                      277,  278,  279,  280,  281,  282,  283,  284,
                                      285,  286,  287,  288,  289,  290,  291,  292,
                                      293,  294,  295,  296,  297,  298,  299,  300,
                                      301,  302,  303,  304,  305,  306,  307,  308,
                                      309,  310,  311,  312,  313,  314,  315,  316,
                                      317,  318,  319,  320,  321,  322,  323,  324,
                                      325,  326,  327,  328,  329,  330,  331,  332,
                                      333,  334,  335,  336,  337,  338,  339,  340,
                                      341,  342,  343,  344,  345,  346,  347,  348,
                                      349,  350,  351,  352,  353,  354,  355,  356,
                                      357,  358,  359,  360,  361,  362,  363,  364,
                                      365,  366,  367,  368,  369,  370,  371,  372,
                                      373,  374,  375,  376,  377,  378,  379,  380,
                                      381,  382,  383,  384,  385,  386,  387,  388,
                                      389,  390,  391,  392,  393,  394,  395,  396,
                                      397,  398,  399,  400,  401,  402,  403,  404,
                                      405,  406,  407,  408,  409,  410,  411,  412,
                                      413,  414,  415,  416,  417,  418,  419,  420,
                                      421,  422,  423,  424,  425,  426,  427,  428,
                                      429,  430,  431,  432,  433,  434,  435,  436,
                                      437,  438,  439,  440,  441,  442,  443,  444,
                                      445,  446,  447,  448,  449,  450,  451,  452,
                                      453,  454,  455,  456,  457,  458,  459,  460,
                                      461,  462,  463,  464,  465,  466,  467,  468,
                                      469,  470,  471,  472,  473,  474,  475,  476,
                                      477,  478,  479,  480,  481,  482,  483,  484,
                                      485,  486,  487,  488,  489,  490,  491,  492,
                                      493,  494,  495,  496,  497,  498,  499,  500,
                                      501,  502,  503,  504,  505,  506,  507,  508,
                                      509,  510,  511,  512,  513,  514,  515,  516,
                                      517,  518,  519,  520,  521,  522,  523,  524,
                                      525,  526,  527,  528,  529,  530,  531,  532,
                                      533,  534,  535,  536,  537,  538,  539,  540,
                                      541,  542,  543,  544,  545,  546,  547,  548,
                                      549,  550,  551,  552,  553,  554,  555,  556,
                                      557,  558,  559,  560,  561,  562,  563,  564,
                                      565,  566,  567,  568,  569,  570,  571,  572,
                                      573,  574,  575,  576,  577,  578,  579,  580,
                                      581,  582,  583,  584,  585,  586,  587,  588,
                                      589,  590,  591,  592,  593,  594,  595,  596,
                                      597,  598,  599,  600,  601,  602,  603,  604,
                                      605,  606,  607,  608,  609,  610,  611,  612,
                                      613,  614,  615,  616,  617,  618,  619,  620,
                                      621,  622,  623,  624,  625,  626,  627,  628,
                                      629,  630,  631,  632,  633,  634,  635,  636,
                                      637,  638,  639,  640,  641,  642,  643,  644,
                                      645,  646,  647,  648,  649,  650,  651,  652,
                                      653,  654,  655,  656,  657,  658,  659,  660,
                                      661,  662,  663,  664,  665,  666,  667,  668,
                                      669,  670,  671,  672,  673,  674,  675,  676,
                                      677,  678,  679,  680,  681,  682,  683,  684,
                                      685,  686,  687,  688,  689,  690,  691,  692,
                                      693,  694,  695,  696,  697,  698,  699,  700,
                                      701,  702,  703,  704,  705,  706,  707,  708,
                                      709,  710,  711,  712,  713,  714,  715,  716,
                                      717,  718,  719,  720,  721,  722,  723,  724,
                                      725,  726,  727,  728,  729,  730,  731,  732,
                                      733,  734,  735,  736,  737,  738,  739,  740,
                                      741,  742,  743,  744,  745,  746,  747,  748,
                                      749,  750,  751,  752,  753,  754,  755,  756,
                                      757,  758,  759,  760,  761,  762,  763,  764,
                                      765,  766,  767,  768,  769,  770,  771,  772,
                                      773,  774,  775,  776,  777,  778,  779,  780,
                                      781,  782,  783,  784,  785,  786,  787,  788,
                                      789,  790,  791,  792,  793,  794,  795,  796,
                                      797,  798,  799,  800,  801,  802,  803,  804,
                                      805,  806,  807,  808,  809,  810,  811,  812,
                                      813,  814,  815,  816,  817,  818,  819,  820,
                                      821,  822,  823,  824,  825,  826,  827,  828,
                                      829,  830,  831,  832,  833,  834,  835,  836,
                                      837,  838,  839,  840,  841,  842,  843,  844,
                                      845,  846,  847,  848,  849,  850,  851,  852,
                                      853,  854,  855,  856,  857,  858,  859,  860,
                                      861,  862,  863,  864,  865,  866,  867,  868,
                                      869,  870,  871,  872,  873,  874,  875,  876,
                                      877,  878,  879,  880,  881,  882,  883,  884,
                                      885,  886,  887,  888,  889,  890,  891,  892,
                                      893,  894,  895,  896,  897,  898,  899,  900,
                                      901,  902,  903,  904,  905,  906,  907,  908,
                                      909,  910,  911,  912,  913,  914,  915,  916,
                                      917,  918,  919,  920,  921,  922,  923,  924,
                                      925,  926,  927,  928,  929,  930,  931,  932,
                                      933,  934,  935,  936,  937,  938,  939,  940,
                                      941,  942,  943,  944,  945,  946,  947,  948,
                                      949,  950,  951,  952,  953,  954,  955,  956,
                                      957,  958,  959,  960,  961,  962,  963,  964,
                                      965,  966,  967,  968,  969,  970,  971,  972,
                                      973,  974,  975,  976,  977,  978,  979,  980,
                                      981,  982,  983,  984,  985,  986,  987,  988,
                                      989,  990,  991,  992,  993,  994,  995,  996,
                                      997,  998,  999, 1000, 1001, 1002, 1003, 1004,
                                     1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012,
                                     1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020,
                                     1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028,
                                     1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036,
                                     1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044,
                                     1045, 1046, 1047, 1048, 1049])

si_long_name = "Si_long"


# %% Set ForceFieldCalculator

# %% ForceFieldCalculator

potentialSet = Tersoff_Si_2005()
calculator = TremoloXCalculator(parameters=potentialSet)


# %% Set Calculator

si_long.setCalculator(calculator)

nlsave('Apply_Heat_Z_Dep_Example_results.hdf5', si_long)


# %% MolecularDynamics

method = NVTNoseHoover()

constraints = [FixStrain(True, True, True), FixAtomConstraints('fixed_layer')]

md_trajectory = MolecularDynamics(
    configuration=si_long,
    constraints=constraints,
    trajectory_filename='Apply_Heat_Z_Dep_Example_results.hdf5',
    steps=10000,
    log_interval=100,
    method=method,
    trajectory_object_id='md',
)
last_image = md_trajectory.lastImage()

nlsave('Apply_Heat_Z_Dep_Example_results.hdf5', last_image, object_id='md_1')


# %% HookFunctions


# Pre-step hook functions
def custom_hook_function(step, time, configuration):
    call_interval = 1
    if step % call_interval != 0:
        return

    # Define a custom script to be run as a hook function in MolecularDynamics.
    # This custom script supports atkpython syntax and can perform almost any
    # procedure.
    from ApplyHeatHook import apply_heat_hook

    pulse_period = 50000  # steps
    pulse_duration = 5  # steps
    heating_rate = 1 * eV / fs
    time_step = 1 * fs
    ramp = True

    configuration = apply_heat_hook(
        configuration, step, time_step, heating_rate, pulse_period, pulse_duration, ramp
    )
    return


pre_step_hooks = [
    custom_hook_function,
]
post_step_hooks = []
measurement_hooks = []
hook_functions = HookFunctions(
    pre_step_hooks=pre_step_hooks,
    post_step_hooks=post_step_hooks,
    measurement_hooks=measurement_hooks,
)

nlsave('Apply_Heat_Z_Dep_Example_results.hdf5', hook_functions)


# %% MolecularDynamics

method = NVTBussiDonadioParrinello(
    initial_velocity=ConfigurationVelocities(),
    reservoir_temperature=[
        ('thermostat_layer', 300.0 * Kelvin),
    ],
)

md_measurement_hook = MDMeasurement(measurements=['temperature'])

constraints = [FixStrain(True, True, True), FixAtomConstraints('fixed_layer')]

md_trajectory_1 = MolecularDynamics(
    configuration=last_image,
    constraints=constraints,
    trajectory_filename='Apply_Heat_Z_Dep_Example_results.hdf5',
    steps=50000,
    log_interval=100,
    method=method,
    hook_functions=hook_functions,
    trajectory_object_id='md_2',
    measurement_hook=md_measurement_hook,
)
last_image_1 = md_trajectory_1.lastImage()

nlsave('Apply_Heat_Z_Dep_Example_results.hdf5', last_image_1, object_id='md_3')

