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 int N = 512; 
int a[N][N];
ll pos[N][N], neg[N][N];
ll dp[N][N];

void solve() {
    int n; cin >> n;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (i!=j) cin >> a[i][j];
        }
    }
    for (int i = 0; i < n; i++) {
        for (int j = i; j >= 0; j--) {
            pos[i][j] += pos[i][j+1] + a[i][j];
            neg[i][j] += neg[i][j+1] + a[j][i];
        }
    }
    memset(dp, 0x3f, sizeof dp);
    dp[0][0] = 0;
    for (int i = 0; i <= n; i++) {
        for (int j = 0; j <= i; j++) {
            ll sum = 0;
            for (int x = i+1; x <= n; x++) {
                //sum += pos[x][j] - pos[x][i];
                sum += -pos[x-1][j];
                sum += neg[x-1][i];
                dp[x][i] = min(dp[x][i], dp[i][j] + sum);
            }
        }
    }
    ll res = 1ll<<60;
    for (int j = 0; j <= n; j++) {
        res = min(res, dp[n][j]);
    }
    for (int i = 0; i < n; i++) {
        res += pos[i][0];
    }
    cout << res;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    solve();
    cout << endl;
}
