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())
X = D-B
Y = C-A

# NYI: WHEN X==0 or Y==0
if X==0:
    print(pow(B,Y,mod))
    exit()
    
if Y==0:
    print(pow(A,X,mod))
    exit()  

dp = [B, A]

for x in range(1,X):
    dp.append(dp[-1]*A%mod)

for y in range(1, Y):
    dp_new = [None]*(X+1)
    dp_new[0] = dp[0]*B%mod

    a = 0
    for x in range(1, X+1):
        a = (a+dp[x-1])*(A+y)%mod
        b = dp[x]*(B+x)%mod
        dp_new[x] = (a+b)%mod

    dp = dp_new
        
    
k = 1
ans = 0
for d in dp[::-1]:
    ans += d*k
    ans %= mod
    k *= C
    k %= mod

print(ans)