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

def fastExponentiation(a,b,N): # Calculates a^b mod N in log b time
    ans = 1
    bDiv2 = b
    aPow2 = a
    while bDiv2 > 0:
        if bDiv2 % 2 != 0:
            ans *= aPow2
            ans %= N
        bDiv2 //= 2
        aPow2 = aPow2 * aPow2
        aPow2 %= N
    return ans

a,b,c,d = map(int,input().split())
DP = []
for i in range(c-a+1):
    DP.append([])
    for j in range(d-b+1):
        DP[i].append(0)

for i in range(c-a+1):
    partialSum = 0
    if i == 0:
        DP[i][0] = 1
        continue
    for j in range(d-b+1):
        if j == 0:
            DP[i][j] = (DP[i-1][j] * b) % MOD
        else:
            partialSum += DP[i-1][j-1]
            partialSum *= (a + i - 1)
            partialSum %= MOD
            DP[i][j] = (DP[i-1][j] * (j + b) + partialSum) % MOD

ans = 0
for j in range(d-b+1):
    ans = ans + DP[c-a][j] * fastExponentiation(c,d-b-j,MOD)
    ans %= MOD
print(ans)