Buggy python submission (verdict: Time Limit Exceeded):
def main():
    A, B, C, D = map(int, input().split())
    mod = 998244353

    dp = [[0]*(D+2) for i in range(C+2)]
    dp[A][B] = 1
    for i in range(A, C+1):
        for j in range(B, D+1):
            ret = dp[i][j]
            if i-A == j-B == 1:
                ret -= (i-1)*(j-1)
            else:
                ret -= dp[i-1][j-1]*(j-1)*(i-1)
            ret %= mod
            dp[i][j] = ret
            dp[i+1][j] += ret * j
            dp[i][j+1] += ret * i

    print(dp[-2][-2])


main()


Fixed submission:
def main():
    A, B, C, D = map(int, input().split())

    c = C - A
    d = D - B
    mod = 998244353
    dp = [[0]*(d+1) for i in range(c+1)]
    dp[0][0] = 1

    for i in range(c+1):

        for j in range(d+1):
            ret = 0
            if i == 0 and j == 0:
                continue
            if i > 0 and j > 0:
                if i == j == 1:
                    ret -= (A+i-1) * (B+j-1)
                else:
                    ret -= dp[i-1][j-1]
                    ret *= (A+i-1)*(B+j-1)
            ret += dp[i-1][j]*(B+j) + dp[i][j-1]*(A+i)

            ret %= mod
            dp[i][j] = ret
    print(dp[c][d])


main()

Buggy python submission (verdict: Time Limit Exceeded):
A, B, C, D = map(int, input().split())
mod = 998244353

dp = [[0]*(D+2) for i in range(C+2)]
dp[A][B] = 1
for i in range(A, C+1):
    for j in range(B, D+1):
        if i-A == j-B == 1:
            dp[i][j] -= (i-1)*(j-1)
        else:
            dp[i][j] -= dp[i-1][j-1]*(j-1)*(i-1)
        dp[i][j] %= mod
        dp[i+1][j] += dp[i][j] * j
        dp[i][j+1] += dp[i][j] * i

print(dp[-2][-2])


Fixed submission:
def main():
    A, B, C, D = map(int, input().split())

    c = C - A
    d = D - B
    mod = 998244353
    dp = [[0]*(d+1) for i in range(c+1)]
    dp[0][0] = 1

    for i in range(c+1):

        for j in range(d+1):
            ret = 0
            if i == 0 and j == 0:
                continue
            if i > 0 and j > 0:
                if i == j == 1:
                    ret -= (A+i-1) * (B+j-1)
                else:
                    ret -= dp[i-1][j-1]
                    ret *= (A+i-1)*(B+j-1)
            ret += dp[i-1][j]*(B+j) + dp[i][j-1]*(A+i)

            ret %= mod
            dp[i][j] = ret
    print(dp[c][d])


main()

Buggy python submission (verdict: Time Limit Exceeded):
def main():
    A, B, C, D = map(int, input().split())

    c = C - A
    d = D - B
    mod = 998244353
    dp = [[0]*(d+1) for i in range(c+1)]
    dp[0][0] = 1

    for i in range(c+1):

        for j in range(d+1):
            ret = 0
            if i == 0 and j == 0:
                continue
            if i > 0 and j > 0:
                if i == j == 1:
                    ret -= (A+i-1) * (B+j-1)
                else:
                    ret -= dp[i-1][j-1]
                    ret *= (A+i-1)*(B+j-1)
            ret += dp[i-1][j]*(B+j) + dp[i][j-1]*(A+i)

            ret %= mod
            dp[i][j] = ret
    print(dp[c][d])


main()



Fixed submission:
def main():
    A, B, C, D = map(int, input().split())

    c = C - A
    d = D - B
    mod = 998244353
    dp = [[0]*(d+1) for i in range(c+1)]
    dp[0][0] = 1

    for i in range(c+1):

        for j in range(d+1):
            ret = 0
            if i == 0 and j == 0:
                continue
            if i > 0 and j > 0:
                if i == j == 1:
                    ret -= (A+i-1) * (B+j-1)
                else:
                    ret -= dp[i-1][j-1]
                    ret *= (A+i-1)*(B+j-1)
            ret += dp[i-1][j]*(B+j) + dp[i][j-1]*(A+i)

            ret %= mod
            dp[i][j] = ret
    print(dp[c][d])


main()

Buggy python submission (verdict: Time Limit Exceeded):
def main():
    A, B, C, D = map(int, input().split())

    c = C - A
    d = D - B
    mod = 998244353
    dp = [[0]*(d+1) for i in range(c+1)]
    dp[0][0] = 1

    for i in range(c+1):
        prev = dp[i-1]
        crr = dp[i]
        if i < c:
            next = dp[i+1]
        for j in range(d+1):
            if i > 0 and j > 0:
                if i == j == 1:
                    crr[j] -= (A+i-1) * (B+j-1)
                else:
                    tmp = prev[j-1]
                    #print(tmp, i, j)
                    tmp *= (A+i-1)*(B+j-1)

                    # print(crr[j], tmp)
                    crr[j] -= tmp

            if i < c:
                next[j] += crr[j]*(B+j)
            if j < d:
                crr[j+1] += crr[j]*(A+i)
            # print(dp)
            crr[j] %= mod

    print(dp[c][d])


main()


Fixed submission:
def main():
    A, B, C, D = map(int, input().split())

    c = C - A
    d = D - B
    mod = 998244353
    dp = [[0]*(d+1) for i in range(c+1)]
    dp[0][0] = 1

    for i in range(c+1):

        for j in range(d+1):
            ret = 0
            if i == 0 and j == 0:
                continue
            if i > 0 and j > 0:
                if i == j == 1:
                    ret -= (A+i-1) * (B+j-1)
                else:
                    ret -= dp[i-1][j-1]
                    ret *= (A+i-1)*(B+j-1)
            ret += dp[i-1][j]*(B+j) + dp[i][j-1]*(A+i)

            ret %= mod
            dp[i][j] = ret
    print(dp[c][d])


main()

Buggy python submission (verdict: Time Limit Exceeded):
def main():
    A, B, C, D = map(int, input().split())
    # 追加の仕方から考えると、塗られている数はC-A + D-B
    # 縦と横の長さが同じなら、その次の動作で塗れる組み合わせは同じ
    # 選びうる方法を全部数え上げよう

    c = C - A
    d = D - B
    mod = 998244353
    dp = [[0]*(d+1) for i in range(c+1)]
    dp[0][0] = 1

    for i in range(c+1):

        for j in range(d+1):
            if i > 0 and j > 0:
                if i == j == 1:
                    dp[i][j] -= (A+i-1) * (B+j-1)
                else:
                    tmp = dp[i-1][j-1]
                    #print(tmp, i, j)
                    tmp *= (A+i-1)*(B+j-1)

                    # print(dp[i][j], tmp)
                    dp[i][j] -= tmp

            if i < c:
                dp[i+1][j] += dp[i][j]*(B+j)
            if j < d:
                dp[i][j+1] += dp[i][j]*(A+i)
            # print(dp)
            dp[i][j] %= mod

    print(dp[c][d])


main()



Fixed submission:
def main():
    A, B, C, D = map(int, input().split())

    c = C - A
    d = D - B
    mod = 998244353
    dp = [[0]*(d+1) for i in range(c+1)]
    dp[0][0] = 1

    for i in range(c+1):

        for j in range(d+1):
            ret = 0
            if i == 0 and j == 0:
                continue
            if i > 0 and j > 0:
                if i == j == 1:
                    ret -= (A+i-1) * (B+j-1)
                else:
                    ret -= dp[i-1][j-1]
                    ret *= (A+i-1)*(B+j-1)
            ret += dp[i-1][j]*(B+j) + dp[i][j-1]*(A+i)

            ret %= mod
            dp[i][j] = ret
    print(dp[c][d])


main()

Buggy python submission (verdict: Time Limit Exceeded):
A, B, C, D = map(int, input().split())
# 追加の仕方から考えると、塗られている数はC-A + D-B
# 縦と横の長さが同じなら、その次の動作で塗れる組み合わせは同じ
# 選びうる方法を全部数え上げよう

c = C - A
d = D - B
mod = 998244353
dp = [[0]*(d+1) for i in range(c+1)]
dp[0][0] = 1

for i in range(c+1):
    for j in range(d+1):
        if i > 0 and j > 0:
            if i == j == 1:
                dp[i][j] -= (A+i-1) * (B+j-1)
            else:
                tmp = dp[i-1][j-1]
                #print(tmp, i, j)
                tmp *= (A+i-1)*(B+j-1)

                # print(dp[i][j], tmp)
                dp[i][j] -= tmp

        if i < c:
            dp[i+1][j] += dp[i][j]*(B+j)
        if j < d:
            dp[i][j+1] += dp[i][j]*(A+i)
        # print(dp)
        dp[i][j] %= mod

print(dp[c][d])

Fixed submission:
def main():
    A, B, C, D = map(int, input().split())

    c = C - A
    d = D - B
    mod = 998244353
    dp = [[0]*(d+1) for i in range(c+1)]
    dp[0][0] = 1

    for i in range(c+1):

        for j in range(d+1):
            ret = 0
            if i == 0 and j == 0:
                continue
            if i > 0 and j > 0:
                if i == j == 1:
                    ret -= (A+i-1) * (B+j-1)
                else:
                    ret -= dp[i-1][j-1]
                    ret *= (A+i-1)*(B+j-1)
            ret += dp[i-1][j]*(B+j) + dp[i][j-1]*(A+i)

            ret %= mod
            dp[i][j] = ret
    print(dp[c][d])


main()

Buggy python submission (verdict: Time Limit Exceeded):
A, B, C, D = map(int, input().split())

c = C - A
d = D - B
mod = 998244353
dp = [[0]*(d+1) for i in range(c+1)]
dp[0][0] = 1

for i in range(c+1):
    for j in range(d+1):
        if i > 0 and j > 0:
            if i == j == 1:
                dp[i][j] -= (A+i-1) * (B+j-1)
            else:
                tmp = dp[i-1][j-1]
                #print(tmp, i, j)
                tmp *= (A+i-1)*(B+j-1)

                # print(dp[i][j], tmp)
                dp[i][j] -= tmp

        if i < c:
            dp[i+1][j] += dp[i][j]*(B+j)
        if j < d:
            dp[i][j+1] += dp[i][j]*(A+i)
        # print(dp)
        dp[i][j] %= mod

print(dp[c][d])

Fixed submission:
def main():
    A, B, C, D = map(int, input().split())

    c = C - A
    d = D - B
    mod = 998244353
    dp = [[0]*(d+1) for i in range(c+1)]
    dp[0][0] = 1

    for i in range(c+1):

        for j in range(d+1):
            ret = 0
            if i == 0 and j == 0:
                continue
            if i > 0 and j > 0:
                if i == j == 1:
                    ret -= (A+i-1) * (B+j-1)
                else:
                    ret -= dp[i-1][j-1]
                    ret *= (A+i-1)*(B+j-1)
            ret += dp[i-1][j]*(B+j) + dp[i][j-1]*(A+i)

            ret %= mod
            dp[i][j] = ret
    print(dp[c][d])


main()