Problem Statement

You are given integers $W,H,L,R,D,U$.

A town of Kyoto is on the two-dimensional plane.

In the town, there is exactly one block at each lattice point $(x,y)$ that satisfies all of the following conditions. There are no blocks at any other points.

• $0\leq x\leq W$
• $0\leq y\leq H$
• $x<L$ or $R<x$ or $y<D$ or $U<y$

Snuke traveled through the town as follows.

• First, he chooses one block and stands there.
• Then, he performs the following operation any number of times (possibly zero):
• Move one unit in the positive direction of the $x$-axis or the positive direction of the $y$-axis. However, the point after moving must also have a block.

Print the number, modulo $998244353$, of possible paths that Snuke could have taken.

Constraints

• $0\leq L\leq R\leq W\leq 10^6$
• $0\leq D\leq U\leq H\leq 10^6$
• There is at least one block.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

W H L R D U

Output

Print the answer.