### regionsBySlashes 
from typing import *
def f_gold(grid: List[str]) -> int:
    def find(x):
        if p[x] != x:
            p[x] = find(p[x])
        return p[x]
    def union(a, b):
        pa, pb = find(a), find(b)
        if pa != pb:
            p[pa] = pb
            nonlocal size
            size -= 1
    n = len(grid)
    size = n * n * 4
    p = list(range(size))
    for i, row in enumerate(grid):
        for j, v in enumerate(row):
            k = i * n + j
            if i < n - 1:
                union(4 * k + 2, (k + n) * 4)
            if j < n - 1:
                union(4 * k + 1, (k + 1) * 4 + 3)
            if v == '/':
                union(4 * k, 4 * k + 3)
                union(4 * k + 1, 4 * k + 2)
            elif v == '\\':
                union(4 * k, 4 * k + 1)
                union(4 * k + 2, 4 * k + 3)
            else:
                union(4 * k, 4 * k + 1)
                union(4 * k + 1, 4 * k + 2)
                union(4 * k + 2, 4 * k + 3)
    return size