Score : $600$ points

Problem Statement

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.
• 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 $998244353$.

1 1 2 2

3

Any two of the three squares other than the bottom-left square can be painted black.

2 1 3 4

65

31 41 59 265

387222020