p02670 AtCoder Grand Contest 044 - Joker
Tonight, in your favourite cinema they are giving the movie Joker and all seats are occupied. In the cinema there are N rows with N seats each, forming an N\times N square. We denote with 1, 2,\dots, N the viewers in the first row (from left to right); with N+1, \dots, 2N the viewers in the second row (from left to right); and so on until the last row, whose viewers are denoted by N^2-N+1,\dots, N^2.

At the end of the movie, the viewers go out of the cinema in a certain order: the i-th viewer leaving her seat is the one denoted by the number P_i. The viewer P_{i+1} waits until viewer P_i has left the cinema before leaving her seat. To exit from the cinema, a viewer must move from seat to seat until she exits the square of seats (any side of the square is a valid exit). A viewer can move from a seat to one of its 4 adjacent seats (same row or same column). While leaving the cinema, it might be that a certain viewer x goes through a seat currently occupied by viewer y; in that case viewer y will hate viewer x forever. Each viewer chooses the way that minimizes the number of viewers that will hate her forever.

Compute the number of pairs of viewers (x, y) such that y will hate x forever.

Constraints

* 2 \le N \le 500
* The sequence P_1, P_2, \dots, P_{N^2} is a permutation of \\{1, 2, \dots, N^2\\}.

Input

The input is given from Standard Input in the format


N
P_1 P_2 \cdots P_{N^2}


Output

If ans is the number of pairs of viewers described in the statement, you should print on Standard Output


ans

Output

If ans is the number of pairs of viewers described in the statement, you should print on Standard Output


ans

Examples

Input

3
1 3 7 9 5 4 8 6 2


Output

1


Input

4
6 7 1 4 13 16 10 9 5 11 12 14 15 2 3 8


Output

3


Input

6
11 21 35 22 7 36 27 34 8 20 15 13 16 1 24 3 2 17 26 9 18 32 31 23 19 14 4 25 10 29 28 33 12 6 5 30


Output

11
```python
import sys
input = sys.stdin.readline
n = int(input())
l = list(map(int,input().split()))
l = [((i-1)//n, (i-1) % n) for i in l]
check = [[1]*n for i in range(n)]
d =  [[min(i, n-i-1, j, n-j-1) for j in range(n)] for i in range(n)]

ans = 0
for x,y in l:
    check[x][y] = 0
    ans += d[x][y]
    q = [(x,y,d[x][y])]
    while q:
        bx,by,z = q.pop()

        if bx != 0:
            if d[bx-1][by] > z:
                d[bx-1][by] = z
                q.append((bx-1,by,z+check[bx-1][by]))
        if bx != n-1:
            if d[bx+1][by] > z:
                d[bx+1][by] = z
                q.append((bx+1,by,z+check[bx+1][by]))
        if by != 0:
            if d[bx][by-1] > z:
                d[bx][by-1] = z
                q.append((bx,by-1,z+check[bx][by-1]))
        if by != n-1:
            if d[bx][by+1] > z:
                d[bx][by+1] = z
                q.append((bx,by+1,z+check[bx][by+1]))  
print(ans)


```