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
#pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
typedef long double ld;
typedef long long ll;
int n;
const int maxN = 505;
ll a[maxN][maxN];
ll dp[maxN][maxN];
ll in_minus[maxN][maxN];
ll in_ones[maxN][maxN];
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    //freopen("input.txt", "r", stdin);
    cin >> n;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (j == i) continue;
            cin >> a[i][j];
        }
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            dp[i][j] = 1e18;
        }
    }
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            if (j > i) {
                in_ones[i][j] = in_ones[i][j - 1];
                in_minus[i][j] = in_minus[i][j - 1];
            }
            // delete all minus ones
            for (int k = i; k < j; k++) {
                in_minus[i][j] += a[k][j];
                in_ones[i][j] += a[j][k];
            }
        }
    }
    for (int last = 0; last < n; last++) {
        dp[0][last] = in_minus[0][last];
    }
    for (int i = 0; i < n; i++) {
        for (int last = 0; last <= i; last++) {
            for (int j = i + 1; j < n; j++) {
                // [last, i], [i + 1, j]
                ll total = in_minus[i + 1][j];
                ll minus_last = in_minus[last][j] - in_minus[last][i] - in_minus[i + 1][j];
                ll one_last = in_ones[last][j] - in_ones[last][i] - in_ones[i + 1][j];
                ll one_all = in_ones[0][j];
                one_all -= in_ones[0][i];
                one_all -= in_ones[i + 1][j];
                one_all -= one_last;
                total += one_all;
                dp[i + 1][j] = min(dp[i + 1][j], dp[last][i] + total);
            }
        }
    }
    ll best = 1e18;
    for (int i = 0; i < n; i++) best = min(best, dp[i][n - 1]);
    cout << best;
    return 0;
}