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;

int main() {
#ifdef LOCAL
  freopen("input.txt", "r", stdin);
#endif
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<vector<long long>> foo(n + 1, vector<long long>(n + 1));
  vector<vector<long long>> bar(n + 1, vector<long long>(n + 1));
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j < i; ++j) {
      cin >> foo[j][i];
    }
    for (int j = i + 1; j <= n; ++j) {
      cin >> bar[i][j];
    }
  }
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= n; ++j) {
      foo[i][j] += foo[i - 1][j] + foo[i][j - 1] - foo[i - 1][j - 1];
      bar[i][j] += bar[i - 1][j] + bar[i][j - 1] - bar[i - 1][j - 1];
    }
  }
  vector<vector<long long>> dp(n + 1, vector<long long>(n + 1, 1ll << 60));
  dp[0][0] = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < max(i, 1); ++j) {
      for (int k = i + 1; k <= n; ++k) {
        long long sum_foo = foo[i][n] + foo[j][k] - foo[i][k] - foo[j][n];
        long long sum_bar = bar[k][k] + bar[i][i] - bar[i][k] - bar[k][i];
        dp[k][i] = min(dp[k][i], dp[i][j] + sum_foo + sum_bar);
      }
    }
  }
  cout << *min_element(dp[n].begin(), dp[n].end()) << "\n";
  return 0;
}
