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
readline = sys.stdin.readline

MOD = 998244353
A, B, C, D = map(int, readline().split())

dp = [[0]*D for _ in range(C)]
dp[A-1][B-1] = 1
for h in range(A, C):
    dp[h][B-1] = dp[h-1][B-1]*B%MOD

for w in range(B, D):
    dp[A-1][w] = dp[A-1][w-1]*A%MOD

for s in range(A+B, C+D-1):
    for h in range(A, C):
        w = s - h
        if not B-1 < w < D:
            continue
        dp[h][w] = (dp[h][w-1] + dp[h-1][w] + dp[h-1][w]*w + dp[h][w-1]*h - dp[h-1][w-1]*h*w)%MOD

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