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, deque
import math
 
# import copy
# from bisect import bisect_left, bisect_right
# import heapq
 
# sys.setrecursionlimit(1000000)
 
# input aliases
input = sys.stdin.readline
 
getS = lambda: input().strip()
getN = lambda: int(input())
getList = lambda: list(map(int, input().split()))
getZList = lambda: [int(x) - 1 for x in input().split()]
 
INF = 10 ** 20
MOD = 998244353
 
def solve():
    a, b, c, d = getList()
    dp = [[1 for i in range(d + 1)] for j in range(c + 1)]
 
    for i in range(a + 1, c + 1):
        dp[i][b] = (dp[i - 1][b] * b) % MOD
    for i in range(b + 1, d + 1):
        dp[a][i] = (dp[a][i - 1] * a) % MOD
 
    for cx in range(a + 1, c + 1):
        for cy in range(b + 1, d + 1):
            dp[cx][cy] = (dp[cx - 1][cy] * cy + dp[cx][cy - 1] * cx - dp[cx - 1][cy - 1] * ((cx - 1) * (cy - 1))) % MOD
            
 
    print(dp[-1][-1])
 
 
def main():
    n = getN()
    for _ in range(n):
        solve()
 
 
if __name__ == "__main__":
    # main()
    solve()