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;

const int N = 502;
typedef long long ll;
const ll inf = 1e18;

ll n , A[N][N] , B[N][N] , dp[N][N] , ans = inf;
ll S(ll x[][N] , int l , int r , int lim) { return x[r][lim] - x[l - 1][lim]; }

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0) , cout.tie(0);
    cin >> n;
    for(int i = 1 ; i <= n ; ++i)
        for(int j = 1 ; j <= n ; ++j)
            if(i < j) cin >> A[i][j];
            else if(i > j) cin >> B[i][j];

    for(int i = 1 ; i <= n ; ++i)
        for(int j = 1 ; j <= n ; ++j) {
            A[i][j] += A[i - 1][j] + A[i][j - 1] - A[i - 1][j - 1];
            B[i][j] += B[i - 1][j] + B[i][j - 1] - B[i - 1][j - 1];
        }
    
    for(int i = 1 ; i < n ; ++i) {
        dp[i][0] = A[i][i];
        for(int j = 1 ; j < i ; ++j) {
            dp[i][j] = inf;
            for(int k = 0 ; k < j ; ++k)
                dp[i][j] = min(dp[i][j] , dp[j][k] + S(A , j + 1 , i , i) + S(B , j + 1 , i , k));
        }
        for(int j = 0 ; j < i ; ++j)
            ans = min(ans , dp[i][j] + S(A , i + 1 , n , n) + S(B , i + 1 , n , j));
    }
    cout << ans << endl;
    return 0;
}