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())
p=998244353
n=c-a+2
m=d-b+2
data=[[0]*(m)for i in range(n)]

data[1][1]=1

#print(data)

for i in range(1,n):
    gyou=a+i-1
    for j in range(1,m):
        retu=b+j-1
        if(i*j==1):
            continue
        data[i][j]=(data[i-1][j]*retu%p)+(data[i][j-1]*gyou%p)-((data[i-1][j-1]*(gyou-1)%p)*(retu-1)%p)
        data[i][j]=data[i][j]%p
        #print(gyou,retu,i,j,data[i][j])
#print(data)
print(data[n-1][m-1]%p)