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;

using ll = long long;

const ll infll = (ll)1e18;
const int N = (int)505;
int n;
ll p_sum_pos[N][N], p_sum_neg[N][N], f[N][N], ans = infll;

ll get_p_sum_pos (int x_1, int x_2, int y_1, int y_2) { return p_sum_pos[x_2][y_2] + p_sum_pos[x_1 - 1][y_1 - 1]
                                                               - p_sum_pos[x_2][y_1 - 1] - p_sum_pos[x_1 - 1][y_2]; }

ll get_p_sum_neg (int x_1, int x_2, int y_1, int y_2) { return p_sum_neg[x_2][y_2] + p_sum_neg[x_1 - 1][y_1 - 1]
                                                               - p_sum_neg[x_2][y_1 - 1] - p_sum_neg[x_1 - 1][y_2]; }

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

//    freopen("test.INP", "r", stdin);

    cin >> n;
    for (int i = 1; i <= n; ++i) {
        for (int j = 1; j < i; ++j) cin >> p_sum_pos[i][j];
        for (int j = i + 1; j <= n; ++j) cin >> p_sum_neg[i][j];
    }

    for (int i = 1; i <= n; ++i) {
        for (int j = 1; j <= n; ++j) {
            p_sum_neg[i][j] += p_sum_neg[i - 1][j] + p_sum_neg[i][j - 1] - p_sum_neg[i - 1][j - 1];
            p_sum_pos[i][j] += p_sum_pos[i - 1][j] + p_sum_pos[i][j - 1] - p_sum_pos[i - 1][j - 1];
        }
    }

    for (int i = 1; i < n; ++i) ans = min(ans, get_p_sum_neg(1, i, 1, i) + get_p_sum_neg(i + 1, n, i + 1, n) );

    for (int i = 1; i < n; ++i) {
        for (int j = i + 1; j < n; ++j) {
            f[i][j] = get_p_sum_pos(j + 1, n, 1, i) + get_p_sum_neg(i + 1, j, i + 1, j) + get_p_sum_neg(1, i, 1, i);
        }
    }

    for (int k = 1; k < n; ++k) {
        for (int i = k + 1; i < n; ++i) {
            for (int j = i + 1; j < n; ++j) {
                f[i][j] = min(f[i][j], f[k][i] + get_p_sum_pos(j + 1, n, k + 1, i) + get_p_sum_neg(i + 1, j, i + 1, j) );
            }
        }
    }

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

    cout << ans;

    return 0;
}
