Buggy python submission (verdict: Time Limit Exceeded):
import sys

sys.setrecursionlimit(10 ** 4)

MOD = 998244353


def solve(A, B, C, D):
    cache = {}

    def numWays(rows, cols):
        if rows == A and cols == B:
            return 1

        key = rows * 4096 + cols
        if key not in cache:

            assert rows >= A and cols >= B
            ways = 0
            if rows > A:
                ways += cols * numWays(rows - 1, cols) % MOD
            if cols > B:
                ways += rows * numWays(rows, cols - 1) % MOD

            if rows > A and cols > B:
                ways -= (cols - 1) * (rows - 1) * numWays(rows - 1, cols - 1) % MOD
            cache[key] = ways % MOD
        return cache[key]

    return numWays(C, D) % MOD


A, B, C, D = [int(x) for x in input().split()]
print(solve(A, B, C, D))


Fixed submission:
MOD = 998244353


def solve(A, B, C, D):
    numWays = [[None for c in range(D + 1)] for r in range(C + 1)]

    numWays[A][B] = 1

    for rows in range(A, C + 1):
        for cols in range(B, D + 1):
            if rows == A and cols == B:
                continue
            ways = 0
            if rows > A:
                ways += cols * numWays[rows - 1][cols] % MOD
            if cols > B:
                ways += rows * numWays[rows][cols - 1] % MOD
            if rows > A and cols > B:
                ways -= (cols - 1) * (rows - 1) * numWays[rows - 1][cols - 1] % MOD
            numWays[rows][cols] = ways % MOD

    return numWays[C][D] % MOD


A, B, C, D = [int(x) for x in input().split()]
print(solve(A, B, C, D))

Buggy python submission (verdict: Time Limit Exceeded):
import sys

sys.setrecursionlimit(10 ** 5)

MOD = 998244353


def solve(A, B, C, D):
    cache = {}

    def numWays(rows, cols):
        if rows == A and cols == B:
            return 1

        key = rows * 4096 + cols
        if key not in cache:

            assert rows >= A and cols >= B
            ways = 0
            if rows > A:
                ways += cols * numWays(rows - 1, cols) % MOD
            if cols > B:
                ways += rows * numWays(rows, cols - 1) % MOD

            if rows > A and cols > B:
                ways -= (cols - 1) * (rows - 1) * numWays(rows - 1, cols - 1) % MOD
            cache[key] = ways % MOD
        return cache[key]

    return numWays(C, D) % MOD


A, B, C, D = [int(x) for x in input().split()]
print(solve(A, B, C, D))


Fixed submission:
MOD = 998244353


def solve(A, B, C, D):
    numWays = [[None for c in range(D + 1)] for r in range(C + 1)]

    numWays[A][B] = 1

    for rows in range(A, C + 1):
        for cols in range(B, D + 1):
            if rows == A and cols == B:
                continue
            ways = 0
            if rows > A:
                ways += cols * numWays[rows - 1][cols] % MOD
            if cols > B:
                ways += rows * numWays[rows][cols - 1] % MOD
            if rows > A and cols > B:
                ways -= (cols - 1) * (rows - 1) * numWays[rows - 1][cols - 1] % MOD
            numWays[rows][cols] = ways % MOD

    return numWays[C][D] % MOD


A, B, C, D = [int(x) for x in input().split()]
print(solve(A, B, C, D))

Buggy python submission (verdict: Time Limit Exceeded):
import sys

from functools import lru_cache

sys.setrecursionlimit(10 ** 5)

MOD = 998244353


def solve(A, B, C, D):
    @lru_cache(maxsize=None)
    def numWays(rows, cols):
        if rows == A and cols == B:
            return 1

        assert rows >= A and cols >= B
        ways = 0
        if rows > A:
            ways += cols * numWays(rows - 1, cols) % MOD
        if cols > B:
            ways += rows * numWays(rows, cols - 1) % MOD

        if rows > A and cols > B:
            ways -= (cols - 1) * (rows - 1) * numWays(rows - 1, cols - 1) % MOD
        return ways % MOD

    return numWays(C, D) % MOD


A, B, C, D = [int(x) for x in input().split()]
print(solve(A, B, C, D))


Fixed submission:
MOD = 998244353


def solve(A, B, C, D):
    numWays = [[None for c in range(D + 1)] for r in range(C + 1)]

    numWays[A][B] = 1

    for rows in range(A, C + 1):
        for cols in range(B, D + 1):
            if rows == A and cols == B:
                continue
            ways = 0
            if rows > A:
                ways += cols * numWays[rows - 1][cols] % MOD
            if cols > B:
                ways += rows * numWays[rows][cols - 1] % MOD
            if rows > A and cols > B:
                ways -= (cols - 1) * (rows - 1) * numWays[rows - 1][cols - 1] % MOD
            numWays[rows][cols] = ways % MOD

    return numWays[C][D] % MOD


A, B, C, D = [int(x) for x in input().split()]
print(solve(A, B, C, D))

Buggy python submission (verdict: Time Limit Exceeded):
import sys

from functools import lru_cache

sys.setrecursionlimit(10 ** 5)

MOD = 998244353


def solve(A, B, C, D):
    @lru_cache(maxsize=None)
    def numWays(rows, cols):
        if rows == A and cols == B:
            return 1
        ways = 0
        if rows > A:
            ways += cols * numWays(rows - 1, cols)
        if cols > B:
            ways += rows * numWays(rows, cols - 1)

        if rows > A and cols > B:
            ways -= (cols - 1) * (rows - 1) * numWays(rows - 1, cols - 1)
        return ways % MOD

    return numWays(C, D) % MOD


A, B, C, D = [int(x) for x in input().split()]
print(solve(A, B, C, D))


Fixed submission:
MOD = 998244353


def solve(A, B, C, D):
    numWays = [[None for c in range(D + 1)] for r in range(C + 1)]

    numWays[A][B] = 1

    for rows in range(A, C + 1):
        for cols in range(B, D + 1):
            if rows == A and cols == B:
                continue
            ways = 0
            if rows > A:
                ways += cols * numWays[rows - 1][cols] % MOD
            if cols > B:
                ways += rows * numWays[rows][cols - 1] % MOD
            if rows > A and cols > B:
                ways -= (cols - 1) * (rows - 1) * numWays[rows - 1][cols - 1] % MOD
            numWays[rows][cols] = ways % MOD

    return numWays[C][D] % MOD


A, B, C, D = [int(x) for x in input().split()]
print(solve(A, B, C, D))