Beautiful Tiling Patterns

In modern architecture, wealthy households often have villas with yards paved in black and white tiles. However, not every tiling is considered aesthetically pleasing. A tiling is regarded as beautiful if there is no 2 × 2 subgrid in which all tiles share the same color. In other words, for any 2 × 2 square in the grid, at least one tile must be different from the others.

Formally, given a grid of size N × M, every cell must be colored either black or white. A tiling is beautiful if for every 2 × 2 block with cells at positions (i, j), (i, j+1), (i+1, j) and (i+1, j+1) (where applicable) the following condition holds:

\[ \text{Not}(a = b = c = d)\] where a, b, c, d represent the colors (0 for white and 1 for black) of the four cells.

Your task is to compute the total number of beautiful tiling schemes for an N × M grid and output the answer modulo a given integer P.

inputFormat

The input consists of a single line with three integers N, M, and P, where:

• N (number of rows)
• M (number of columns)
• P (the modulus)

You may assume that N and M are positive integers.

outputFormat

Output a single integer representing the number of beautiful tiling schemes modulo P.

sample

1 1 100

2