Extension

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

inputFormat

Input

Input is given from Standard Input in the following format:

A B C D

outputFormat

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

样例

2 1 3 4

65