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
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

A, B, C, D = mapint()
mod = 998244353

dp = [[0]*D for _ in range(C)]
dp[A-1][B-1] = 1

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

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