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 <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
#include <fstream>
#include <utility>
#include <functional>
#include <time.h>
#include <stack>
#include <array>
#define popcount __builtin_popcount
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;
int n;
int a[505][505];
ll s1[505][505], s2[505][505];
ll dp[2][505][505];
int main()
{
    cin>>n;
    for(int i=0; i<n; i++){
        for(int j=0; j<n; j++){
            if(i==j) continue;
            cin>>a[i][j];
        }
    }
    for(int i=0; i<n; i++){
        for(int j=0; j<n; j++) s1[i][j+1]=s1[i][j]+a[i][j];
        for(int j=0; j<n; j++) s2[i][j+1]=s2[i][j]+a[j][i];
    }
    const ll INF=1e18;
    dp[0][0][1]=0;
    for(int i=1; i<n; i++){
        for(int j=0; j<=i+1; j++) for(int k=1; j+k<=i+1; k++) dp[i&1][j][k]=INF;
        for(int j=0; j<=i; j++){
            for(int k=1; j+k<=i; k++){
                if(dp[(i&1)^1][j][k]==INF) continue;
                dp[i&1][j][k+1]=min(dp[i&1][j][k+1], dp[(i&1)^1][j][k]+s2[i][i]-s2[i][i-k]+s1[i][i-j-k]);
                dp[i&1][k][1]=min(dp[i&1][k][1], dp[(i&1)^1][j][k]+s1[i][i-k]);
                dp[i&1][0][1]=min(dp[i&1][0][1], dp[(i&1)^1][j][k]+s1[i][i]);
            }
        }
    }
    ll ans=INF;
    for(int i=0; i<=n; i++){
        for(int j=1; i+j<=n; j++) ans=min(ans, dp[(n-1)&1][i][j]);
    }
    cout<<ans<<endl;
    return 0;
}
