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
import math
import fractions
from collections import deque
from collections import defaultdict
sys.setrecursionlimit(10**7)

A, B, C, D = map(int, input().split())
mod = 998244353

dp = [[0]*(D+1) for _ in range(C+1)]
dp[A][B] = 1
for i in range(A, C):
    dp[i+1][B] = dp[i][B] * B % mod

for i in range(B, D):
    dp[A][i+1] = dp[A][i] * A % mod


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

print(dp[C][D])