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;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}
using Int = long long;
const char newl = '\n';

//INSERT ABOVE HERE
const Int MAX = 505;
const Int INF = 1e18;
Int A[MAX][MAX];
Int dp[MAX][MAX];

Int X[MAX][MAX];
Int Y[MAX][MAX];

signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  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];

  memset(X,0,sizeof(X));
  for(Int k=1;k<n;k++){
    for(Int i=0;i<k;i++){
      if(i) X[k][i]=X[k][i-1];
      Int a=i;
      for(Int b=k+1;b<n;b++)
        X[k][i]+=A[b][a];
    }
  }

  memset(Y,0,sizeof(Y));
  for(Int k=1;k<n;k++){
    for(Int i=k-1;i>=0;i--){
      Y[k][i]=Y[k][i+1];
      Int a=i;
      for(Int b=a+1;b<=k;b++)
        Y[k][i]+=A[a][b];
    }
  }

  for(Int i=0;i<MAX;i++)
    for(Int j=0;j<MAX;j++)
      dp[i][j]=INF;

  for(Int k=1;k<n;k++)
    for(Int i=0;i<k;i++)
      dp[k][i]=X[k][i]+Y[k][i+1]+Y[i][0];

  for(Int i=0;i+1<n;i++)
    for(Int j=0;j<i;j++)
      for(Int k=i+1;k+1<n;k++)
        chmin(dp[k][i],dp[i][j]+(X[k][i]-X[k][j])+Y[k][i+1]);

  Int ans=INF;
  for(Int k=0;k+1<n;k++){
    Int tmp=0;
    for(Int a=0;a<n;a++)
      for(Int b=a+1;b<n;b++)
        if(a<=k and k<b) continue;
        else tmp+=A[a][b];
    chmin(ans,tmp);
  }

  for(Int i=0;i+1<n;i++)
    for(Int j=0;j<i;j++)
      chmin(ans,dp[i][j]+Y[n-1][i+1]);

  cout<<ans<<endl;
  return 0;
}
