Problem: We have a grid with A horizontal rows and B vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation:

* Assume that the grid currently has a horizontal rows and b vertical columns. Choose "vertical" or "horizontal".
* If we choose "vertical", insert one row at the top of the grid, resulting in an (a+1) \times b grid.
* If we choose "horizontal", insert one column at the right end of the grid, resulting in an a \times (b+1) grid.
* Then, paint one of the added squares black, and the other squares white.



Assume the grid eventually has C horizontal rows and D vertical columns. Find the number of ways in which the squares can be painted in the end, modulo 998244353.

Constraints

* 1 \leq A \leq C \leq 3000
* 1 \leq B \leq D \leq 3000
* A, B, C, and D are integers.

Input

Input is given from Standard Input in the following format:


A B C D


Output

Print the number of ways in which the squares can be painted in the end, modulo 998244353.

Examples

Input

1 1 2 2


Output

3


Input

2 1 3 4


Output

65


Input

31 41 59 265


Output

387222020

Solution (in PYTHON3):

Solution:
import sys
from collections import defaultdict

def solve():
    input = sys.stdin.readline
    A, B, C, D = map(int, input().split())
    mod = 998244353

    DP = [[0 for j in range(D + 1)] for i in range(C + 1)]
    DP[A][B] = 1
    for b in range(B + 1, D + 1):
        DP[A][b] = (DP[A][b-1] * A) % mod
    
    for a in range(A + 1, C + 1):
        DP[a][B] = (DP[a-1][B] * B) % mod
        for b in range(B + 1, D + 1):
            DP[a][b] = ((DP[a][b-1] * a) % mod + (DP[a-1][b] * b) % mod - (DP[a-1][b-1] * (a-1) * (b-1)) % mod) % mod
    print(DP[C][D])
    #print(DP)

    return 0

if __name__ == "__main__":
    solve()