Problem Description: Rules of the game: To apply one step of the rules, you have to count the number of live neighbors for each cell. What happens next depends on this number.

A dead cell with exactly three live neighbors becomes a live cell $($birth$).$

A live cell with two or three live neighbors stays alive $($survival$).$

In all other cases, a cell dies or remains dead $($overcrowding or loneliness$).$

Note: The number of live neighbors is always based on the cells before the rule was applied. In other words, you must first find all of the cells that change before changing any of them.

Data Structure: Two$-$dimensional array$/$ Vector

Sample Input: