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

Input

3
010
111
010

Output

12

Example 2

Input

4
0110
1110
0000
0110

Output

16

Example 3

Input

2
01
10

Output

8

Python Template

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