Introduction

Conway's Game of Life is a fascinating cellular automaton created by the British mathematician John Horton Conway in 1970.

The game consists of a two-dimensional grid of cells that can either be "alive" or "dead."

After each generation, the cells interact with their eight neighbors via a set of rules, which define the new generation.

Instructions

After each generation, the cells interact with their eight neighbors, which are cells adjacent horizontally, vertically, or diagonally.

The following rules are applied to each cell:

Given a matrix of 1s and 0s (corresponding to live and dead cells), apply the rules to each cell, and return the next generation.

Each row of the grid is represented as a 64 bit integer.

For example,

    0 1 0
    1 0 0
    1 1 0

is represented as

0b010
0b100
0b110

The grid has at most 64 columns.