# Time:  O(n^2)
# Space: O(n^2)

class UnionFind(object):
    def __init__(self, n):
        self.set = range(n)
        self.count = n

    def find_set(self, x):
       if self.set[x] != x:
           self.set[x] = self.find_set(self.set[x])  # path compression.
       return self.set[x]

    def union_set(self, x, y):
        x_root, y_root = map(self.find_set, (x, y))
        if x_root != y_root:
            self.set[min(x_root, y_root)] = max(x_root, y_root)
            self.count -= 1


class Solution(object):
    def regionsBySlashes(self, grid):
        """
        :type grid: List[str]
        :rtype: int
        """
        def index(n, i, j, k):
            return (i*n + j)*4 + k
    
        union_find = UnionFind(len(grid)**2 * 4)
        N, E, S, W = range(4)
        for i in xrange(len(grid)):
            for j in xrange(len(grid)):
                if i:
                    union_find.union_set(index(len(grid), i-1, j, S),
                                         index(len(grid),i, j, N))
                if j:
                    union_find.union_set(index(len(grid), i, j-1, E),
                                         index(len(grid), i, j, W))
                if grid[i][j] != "/":
                    union_find.union_set(index(len(grid), i, j, N),
                                         index(len(grid), i, j, E))
                    union_find.union_set(index(len(grid), i, j, S),
                                         index(len(grid), i, j, W))
                if grid[i][j] != "\\":
                    union_find.union_set(index(len(grid), i, j, W),
                                         index(len(grid), i, j, N))
                    union_find.union_set(index(len(grid), i, j, E),
                                         index(len(grid), i, j, S))
        return union_find.count