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())
m = c-a
n = d-b
t = [[1]]
for i in range(m):
    t[0].append((b*t[0][i])%998244353)
for i in range(n):
    t.append([(a*t[i][0])%998244353]+[0]*m)
for i in range(1,n+1):
    for j in range(1,m+1):
        t[i][j] = t[i][j-1]*(b+i) + t[i-1][j]*(a+j) - t[i-1][j-1]*((a+j-1)*(b+i-1))
        t[i][j] %= 998244353
print(t[n][m])