Problem Statement

There is a shogi board with $H \times W$ rows and columns and $1$ silver general piece.

As shown in Figure $1$, a silver general can move to the $3$ squares in front of it and to the squares diagonally behind it. However, the destination must be inside the board.

More precisely, denoting the square in the $i$-th row from the top and the $j$-th column from the left by $(i,j)$, a silver placed on $(i,j)$ can move to $(i-1,j-1),(i-1,j),(i-1,j+1),(i+1,j-1),(i+1,j+1)$.

Moving the silver general so that the following condition is satisfied is called a "silver full-board tour".

• Place the silver on one of the squares in the bottom row of the board, that is, one of $(H,j)$ $(1 \leq j \leq W)$, and move the silver so that it passes through all squares without passing through the same square more than once.

For example, the moves shown in Figure $2$ are one example of a silver full-board tour when $H = W = 2$.

Find the number of possible silver full-board tours, modulo $M$.
Here, two silver full-board tours are considered different if they differ when the moves are viewed as sequences of squares.

Constraints

• All inputs are integers.
• $1 \leq H \leq 50$
• $1 \leq W \leq 50$
• $9 \times 10^8 \leq M \leq 10^9$

Input

$H\ W\ M$

Output

Output the answer in $1$ line.

Sample

2 2 998244353

2

9 9 998244353

0

6 5 924844033

60

50 50 1000000000

999575486