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;

void chmin(int64_t& a, int64_t b){
    a = min(a, b);
}

int main(){
    int N;
    int64_t A[500][500] = {0}, Spos[501][501] = {0}, Sneg[501][501] = {0};
    cin >> N;
    for(int i=0; i<N; i++) for(int j=0; j<N; j++) if(i!=j){
        cin >> A[i][j];
        (i < j ? Sneg[i+1][j+1] : Spos[i+1][j+1]) = A[i][j];
    }

    for(int i=0; i<N; i++) for(int j=0; j<N; j++){
        Spos[i+1][j+1] += Spos[i+1][j] + Spos[i][j+1] - Spos[i][j];
        Sneg[i+1][j+1] += Sneg[i+1][j] + Sneg[i][j+1] - Sneg[i][j];
    }

    const int64_t INF = 1e18;
    int64_t dp[501][501];
    for(int i=0; i<=N; i++) for(int j=0; j<=N; j++) dp[i][j] = INF;
    dp[N][N] = 0;
    for(int i=N; i>=0; i--) for(int j=N; j>=i; j--) for(int k=i-1; k>=0; k--){
        int64_t res = dp[i][j];
        res += Sneg[i][i] - Sneg[i][k] - Sneg[k][i] + Sneg[k][k];
        res += Spos[N][i] - Spos[N][k] - Spos[j][i] + Spos[j][k];
        chmin(dp[k][i], res);
    }

    int64_t ans = INF;
    for(int j=0; j<=N; j++) chmin(ans, dp[0][j]);
    cout << ans << endl;
    return 0;
}
