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:
import sys,collections as cl,bisect as bs
sys.setrecursionlimit(100000)
input = sys.stdin.readline
mod = 998244353
Max = sys.maxsize
def l(): #intのlist
	return list(map(int,input().split()))
def m(): #複数文字
	return map(int,input().split())
def onem(): #Nとかの取得
	return int(input())
def s(x): #圧縮
	a = []
	if len(x) == 0:
		return []
	aa = x[0]
	su = 1
	for i in range(len(x)-1):
		if aa != x[i+1]:
			a.append([aa,su])
			aa = x[i+1]
			su = 1
		else:
			su += 1
	a.append([aa,su])
	return a
def jo(x): #listをスペースごとに分ける
	return " ".join(map(str,x))
def max2(x): #他のときもどうように作成可能
	return max(map(max,x))
def In(x,a): #aがリスト(sorted)
    k = bs.bisect_left(a,x)
    if k != len(a) and a[k] ==  x:
        return True
    else:
        return False

def pow_k(x, n):
    ans = 1
    while n:
        if n % 2:
            ans *= x
        x *= x
        n >>= 1
    return ans

"""
def nibu(x,n,r):
	ll = 0
	rr = r
	while True:
		mid = (ll+rr)//2

	if rr == mid:
		return ll
	if (ここに評価入れる):
		rr = mid
	else:
		ll = mid+1
"""

a,b,c,d = m()

ans = 0

po = c-a

poo = d-b
dp = [[0 for i in range(poo+1)]for j in range(po+1)]
dp[0][0] = 1
for i in range(po+1):
	for j in range(poo+1):
		if i == 0:
			if j != 0:
				dp[i][j] = dp[i][j-1] * a
				dp[i][j] %= mod
		else:
			if j == 0:
				dp[i][j] = dp[i-1][j] * b
				dp[i][j] %= mod
			else:
				dp[i][j] = dp[i-1][j] * (b+j) + dp[i][j-1] * (a+i) - (a+i-1)*(b+j-1)*dp[i-1][j-1]
				dp[i][j] %= mod
print(dp[-1][-1])