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())
MOD = 998244353
dp = [[0]*D for i in range(C)]
dp[A-1][B-1] = 1

for i in range(C):
    for j in range(D):
        if i!=A-1 or j!=B-1:
            val1 = dp[i-1][j]*(j+1)
            if i==0:
                val1 = 0
            val2 = dp[i][j-1]*(i+1)
            if j==0:
                val2 = 0
            val3 = 0
            if val1*val2!=0:
                val3 = i*j
            dp[i][j] = (val1+val2 - val3*dp[i-1][j-1])%MOD
            #dp[i][j] = (dp[i-1][j]*(j+1) + dp[i][j-1]*(i+1) - i*j)%MOD
# print(dp)
print(dp[C-1][D-1])