Problem Statement

You are given positive integers $N$, $H$, and $W$, with $H,W \le 3N-1$.

Find the number, modulo $998244353$, of ways to place four $N\times N$ square tiles on an $H\times W$ grid that satisfy all of the following conditions.

• Each tile exactly covers $N^2$ cells of the grid.
• No cell is covered by more than one tile.

Here, the tiles are indistinguishable.

There are $T$ test cases; solve each one.

Constraints

• $1\le T\le 2\times 10^5$
• $1\le N,H,W\le 10^9$
• $H,W\le 3N-1$
• All input values are integers.

Input

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

T
\text{case}_1
\vdots
\text{case}_T

Each case is given in the following format:

N H W

Output

Print $T$ lines. The $i$-th line should contain the number, modulo $998244353$, of valid ways to place the tiles for the $i$-th test case.