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:
mod=998244353
a,b,c,d=map(int,input().split())
if a==c and b==d:
  print(1)
  exit()
dp=[[0]*d for _ in range(c)]
tmp=1
for i in range(a,c):
  tmp*=b
  tmp%=mod
  dp[i][b-1]=tmp
tmp=1
for i in range(b,d):
  tmp*=a
  tmp%=mod
  dp[a-1][i]=tmp
for i in range(b,d):
  tmp=0
  for j in range(a,c):
    tmp*=i
    tmp+=dp[j-1][i]
    tmp%=mod
    dp[j][i]=tmp+(j+1)*dp[j][i-1]
    dp[j][i]%=mod
print(dp[c-1][d-1])