We have a weighted directed graph with N vertices numbered 0 to N-1.

The graph initially has N-1 edges. The i-th edge (0 \leq i \leq N-2) is directed from Vertex i to Vertex i+1 and has a weight of 0.

Snuke will now add a new edge (i → j) for every pair i, j (0 \leq i,j \leq N-1,\ i \neq j). The weight of the edge will be -1 if i < j, and 1 otherwise.

Ringo is a boy. A negative cycle (a cycle whose total weight is negative) in a graph makes him sad. He will delete some of the edges added by Snuke so that the graph will no longer contain a negative cycle. The cost of deleting the edge (i → j) is A_{i,j}. He cannot delete edges that have been present from the beginning.

Find the minimum total cost required to achieve Ringo's objective.

Constraints

* 3 \leq N \leq 500
* 1 \leq A_{i,j} \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_{0,1} A_{0,2} A_{0,3} \cdots A_{0,N-1}
A_{1,0} A_{1,2} A_{1,3} \cdots A_{1,N-1}
A_{2,0} A_{2,1} A_{2,3} \cdots A_{2,N-1}
\vdots
A_{N-1,0} A_{N-1,1} A_{N-1,2} \cdots A_{N-1,N-2}


Output

Print the minimum total cost required to achieve Ringo's objective.

Examples

Input

3
2 1
1 4
3 3


Output

2


Input

4
1 1 1
1 1 1
1 1 1
1 1 1


Output

2


Input

10
190587 2038070 142162180 88207341 215145790 38 2 5 20
32047998 21426 4177178 52 734621629 2596 102224223 5 1864
41 481241221 1518272 51 772 146 8805349 3243297 449
918151 126080576 5186563 46354 6646 491776 5750138 2897 161
3656 7551068 2919714 43035419 495 3408 26 3317 2698
455357 3 12 1857 5459 7870 4123856 2402 258
3 25700 16191 102120 971821039 52375 40449 20548149 16186673
2 16 130300357 18 6574485 29175 179 1693 2681
99 833 131 2 414045824 57357 56 302669472 95
8408 7 1266941 60620177 129747 41382505 38966 187 5151064


Output

2280211
#include <bits/stdc++.h>
using namespace std;
const long long oo = 1LL << 60;

int n;
long long a[555][555], sum[555][555];

long long sumRect(int x, int y, int xx, int yy)
{
  return a[xx][yy] + a[x][y] - a[x][yy] - a[xx][y];
}

int main()
{
  ios::sync_with_stdio(0);
  cin.tie(0);

  cin >> n;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++)
    {
      int x = 0;
      if (i != j)
        cin >> x;
      a[i][j] = a[i - 1][j] + a[i][j - 1] - a[i - 1][j - 1] + x;
    }

  for (int i = 0; i < n; i++)
    for (int j = i + 1; j <= n; j++)
      sum[i][j] = sum[i][j - 1] + sumRect(i, j - 1, j - 1, j);

  long long ans = 0;
  for (int i = 1; i <= n; i++)
    ans += sumRect(i - 1, i, i, n);

  long long f[555][555];
  for (int i = 0; i < n; i++)
    for (int j = i; j < n; j++)
      f[i][j] = oo;

  for (int i = 1; i < n; i++)
    f[0][i] = sum[0][i];

  for (int i = 0; i < n; i++)
    for (int j = i + 1; j < n; j++)
    {
      ans = min(ans, f[i][j] + sum[j][n]);
      for (int k = j + 1; k < n; k++)
        f[j][k] = min(f[j][k], f[i][j] + sum[j][k] + sumRect(k, i, n, j));
    }

  cout << ans << endl;
}
