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:
M = 998244353

A, B, C, D = map(int, input().split())

table_a = [None] * (D - B + 1)
table_h = [None] * (D - B + 1)
table_v = [None] * (D - B + 1)

tmp_table_a = [None] * (D - B + 1)
tmp_table_h = [None] * (D - B + 1)
tmp_table_v = [None] * (D - B + 1)

table_a[0] = 1

c = 1
for x in range(1, D - B + 1):
	c = (c * A) % M
	table_a[x] = c
	table_v[x] = c

#c = 1
#for y in range(1, C - A + 1):
#	c = (c * B) % M
#	table_a[y][0] = c
#	table_h[y][0] = c

c = 1
for y in range(1, C - A + 1):
	c = (c * B) % M
	
	tmp_table_a[0] = c
	tmp_table_h[0] = c
	
	for x in range(1, D - B + 1):
#		print(x, y, table[y - 1][x] * (B + x - 1), table[y][x - 1] * (A + y - 1))
#		table[y][x] = table[y - 1][x] * (B + x - 1) + table[y - 1][x - 1] * (B + x - 1 + A + y - 1)
#		table[y][x] = max(table[y - 1][x] * (B + x - 1),  table[y][x - 1] * (A + y - 1)) + table[y - 1][x - 1] * (B + x - 1 + A + y - 1)
		
		tmp_table_v[x] = (tmp_table_a[x - 1] * (A + y)) % M
		tmp_table_h[x] = (table_a[x] * (B + x)) % M
		tmp_table_a[x] = (tmp_table_h[x] + (tmp_table_a[x - 1] - tmp_table_h[x - 1]) * (A + y) + tmp_table_h[x - 1]) % M
	
	table_a, tmp_table_a = (tmp_table_a, table_a)
	table_v, tmp_table_v = (tmp_table_v, table_v)
	table_h, tmp_table_h = (tmp_table_h, table_h)
	
#print(table_a)
#print(table_v)
#print(table_h)

print(table_a[D - B])