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:
# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline

a,b,c,d = map(int,readline().split())


dp1 = [[0]*(d+1) for _ in range(c+1)] #下OK
dp2 = [[0]*(d+1) for _ in range(c+1)] #下NG

dp1[a][b] = 1

#print(dp1)
#print(dp2)
MOD = 998244353
for i in range(a,c+1):
    for j in range(b,d+1):
        if i != c:
            dp1[i+1][j] += j*dp1[i][j]
            dp1[i+1][j] += dp2[i][j]
            dp1[i+1][j] %= MOD
        if j != d:
            dp2[i][j+1] += i*dp2[i][j]
            dp2[i][j+1] += i*dp1[i][j]
            dp2[i][j+1] %= MOD
            
#print(dp1)
#print(dp2)

print((dp1[c][d]+dp2[c][d])%MOD)