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 - b + 1) for _ in range(c - a + 1)]

dp[0][0] = 1

for x in range(1, d - b + 1):
    dp[0][x] = dp[0][x - 1] * a % MOD
for y in range(1, c - a + 1):
    dp[y][0] = dp[y - 1][0] * b % MOD

for x in range(1, c - a + 1):
    for y in range(1, d - b + 1):
        dp[x][y] = (dp[x - 1][y] * (b + y) + dp[x][y - 1] * (a + x) - dp[x - 1][y - 1] * (a + x - 1) * (b + y - 1)) % MOD

print(dp[-1][-1])