Number of Valid Move Combinations On Chessboard LeetCode solution in Python

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class Solution:
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    def countCombinations(self, pieces: List[str], positions: List[List[int]]) -> int:
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        board = [[set() for _ in range(8)] for _ in range(8)]
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        n = len(pieces)
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        for pos in positions:
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            pos[0] -= 1
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            pos[1] -= 1
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        all_time = set(range(1, 8))
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        def recur(i):
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            if i == n:
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                return 1
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            ans = 0
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            line = [(0, 1), (1, 0), (0, -1), (-1, 0)]
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            diag = [(1, 1), (1, -1), (-1, 1), (-1, -1)]
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            r, c = positions[i]
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            if not board[r][c] & all_time:
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                board[r][c] |= all_time
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                ans += recur(i + 1)
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                board[r][c].clear()
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            directions = []
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            if pieces[i] in ("queen", "rook"):
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                directions.extend(line)
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            if pieces[i] in ("queen", "bishop"):
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                directions.extend(diag)
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            for dr, dc in directions:
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                x, y = r + dr, c + dc
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                count = 1
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                while 0 <= x < 8 and 0 <= y < 8 and count not in board[x][y]:
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                    board[x][y].add(count)
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                    count += 1
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                    rest = set(range(count, 8))
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                    if not board[x][y] & rest:
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                        board[x][y] |= rest
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                        ans += recur(i + 1)
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                        board[x][y] -= rest
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                    x += dr
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                    y += dc
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                count -= 1
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                x -= dr
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                y -= dc
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                while count:
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                    board[x][y].remove(count)
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                    count -= 1
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                    x -= dr
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                    y -= dc
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            return ans
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        return recur(0)