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:
#!/usr/bin/env python3
import sys
input = sys.stdin.readline

a, b, c, d = map(int, input().split())
dp = [[0] * (d - b + 1) for _ in range(c - a + 1)]

dp[0][0] = 1
for i in range(c - a + 1):
    for j in range(d - b + 1):
        if i > 0:
            dp[i][j] += dp[i-1][j] * (b+j)
        if j > 0:
            dp[i][j] += dp[i][j-1] * (a+i)
        if i > 0 and j > 0:
            dp[i][j] -= dp[i-1][j-1] * (b+j-1) * (a+i-1)
        dp[i][j] %= 998244353

print(dp[-1][-1])