Perimeter

Problem Statement

You have a square grid with length $n$. Each cell in the grid can be either $1$ or $0$.

Return the length of the perimeter required to surround all the $1$ cells in the grid.

Input

Your first line will contain $n$.

Your next $n$ lines will each contain $n$ grids of $1$'s and $0$s.

Output

A single integer representing the unit perimeter required to surround all the $1$ cells in the grid.

Constraints

For all test cases:

• $1 \le n \le 10^3$
• All cells will be either $1$ or $0$.

Example 1

3
010
111
010

12

Example 2

4
0110
1110
0000
0110

16

Example 3

2
01
10

8

Python Template

n = int(input())
grid = [list(map(int, input())) for _ in range(n)]