Given a rows x cols matrix mat, where mat[i][j] is either 0 or 1, return the number of special positions in mat.
A position (i,j) is called special if mat[i][j] == 1 and all other elements in row i and column j are 0 (rows and columns are 0-indexed).
Example 1:
Input: mat = [[1,0,0],
              [0,0,1],
              [1,0,0]]
Output: 1
Explanation: (1,2) is a special position because mat[1][2] == 1 and all other elements in row 1 and column 2 are 0.
Example 2:
Input: mat = [[1,0,0],
              [0,1,0],
              [0,0,1]]
Output: 3
Explanation: (0,0), (1,1) and (2,2) are special positions. 
Example 3:
Input: mat = [[0,0,0,1],
              [1,0,0,0],
              [0,1,1,0],
              [0,0,0,0]]
Output: 2
Example 4:
Input: mat = [[0,0,0,0,0],
              [1,0,0,0,0],
              [0,1,0,0,0],
              [0,0,1,0,0],
              [0,0,0,1,1]]
Output: 3
Constraints:
rows == mat.length
cols == mat[i].length
1 <= rows, cols <= 100
mat[i][j] is 0 or 1.
class Solution:
    def numSpecial(self, mat: List[List[int]]) -> int:
        ## My original solution, not very fast
        # mat_t = list(zip(*mat))
        # row_s = [i for i in range(len(mat)) if sum(mat[i]) == 1]
        # col_s = [j for j in range(len(mat_t)) if sum(mat_t[j]) == 1]
        # return sum(mat[i][j] == 1 and i in row_s and j in col_s for i in range(len(mat)) for j in range(len(mat_t)))
        
        ## Modified version, still not very fast
        mat_t = list(zip(*mat))
        res = 0
        for i in range(len(mat)):
            for j in range(len(mat_t)):
                if mat[i][j] == sum(mat[i]) == sum(mat_t[j]) == 1:
                    res += 1
        return res
class Solution:
    def numSpecial(self, mat: List[List[int]]) -> int:
        ## My original solution, not very fast
        # mat_t = list(zip(*mat))
        # row_s = [i for i in range(len(mat)) if sum(mat[i]) == 1]
        # col_s = [j for j in range(len(mat_t)) if sum(mat_t[j]) == 1]
        # return sum(mat[i][j] == 1 and i in row_s and j in col_s for i in range(len(mat)) for j in range(len(mat_t)))
        
        ## Modified version, still not very fast
        mat_t = list(zip(*mat))
        res = 0
        for i in range(len(mat)):
            for j in range(len(mat_t)):
                if mat[i][j] == sum(mat[i]) == sum(mat_t[j]) == 1:
                    res += 1
        return res