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:
a,b,c,d=map(int,input().split())
def amari(a):
  return a % 998244353
X0=[[0]*d for i in range(c)]
X1=[[0]*d for i in range(c)]
X2=[[0]*d for i in range(c)]
X0[a-1][b-1]=1
for j in range(b,d):
 X0[a-1][j]=amari(X0[a-1][j-1]*(a-1))
 X1[a-1][j]=amari(X0[a-1][j-1]+X1[a-1][j-1]*(a-1))
 X2[a-1][j]=amari(X1[a-1][j-1]+X2[a-1][j-1]*a)
for i in range(a,c):
 for j in range(b,d+1):
  X1[i][j-1]=amari((X0[i-1][j-1]+X1[i-1][j-1]+X2[i-1][j-1])*j)
  if j>=2:
   X2[i][j-1]=amari(X1[i][j-2]+X2[i][j-2] *(i+1))
print(amari(X0[c-1][d-1]+X1[c-1][d-1]+X2[c-1][d-1]))