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 <iostream>
#include <iomanip>
#include <cstdio>
#include <vector>
#include <string>
#include <algorithm>
#include <map>
#include <set>
 
using namespace std;
typedef long long ll;
const int MAXN = 510;

int N;
ll A[MAXN][MAXN];
ll ps[MAXN][MAXN];
ll vs[MAXN][MAXN];
ll dp[MAXN][MAXN]; // size of cur comp, prev comp
ll ndp[MAXN][MAXN];

int main()
{
    ios_base::sync_with_stdio(0);

    cin >> N;
    for (int i = 0; i < N; i++)
    {
        for (int j = 0; j < N; j++)
        {
            if (j == i) A[i][j] = 0;
            else cin >> A[i][j];
        }
    }

    for (int i = 0; i < N; i++)
    {
        ps[i][0] = 0;
        for (int j = 0; j < N; j++)
            ps[i][j+1] = ps[i][j] + A[i][j];
        vs[i][0] = 0;
        for (int j = 0; j < N; j++)
            vs[i][j+1] = vs[i][j] + A[j][i];
    }

    for (int i = 0; i < MAXN; i++)
        for (int j = 0; j < MAXN; j++)
            dp[i][j] = 1e17;
    dp[0][0] = 0;
    for (int i = 0; i < N; i++)
    {
        for (int j = 0; j <= N; j++)
            for (int k = 0; k <= N; k++)
                ndp[j][k] = 1e17;

        for (int j = 0; j <= i; j++)
        {
            for (int k = 0; k <= i - j; k++)
            {
                if (dp[j][k] > 9e16) continue;

                int ostart = i - j;
                int mstart = i - j - k;

                // route 1, join comp
                ll rtot = 0;
                rtot += vs[i][i] - vs[i][ostart];
                rtot += ps[i][mstart];
                ndp[j+1][k] = min (ndp[j+1][k], dp[j][k] + rtot);

                // route 2, start new
                rtot = 0;
                rtot += ps[i][ostart];
                ndp[1][j] = min (ndp[1][j], dp[j][k] + rtot);
            }
        }

        for (int j = 0; j <= N; j++)
            for (int k = 0; k <= N; k++)
                dp[j][k] = ndp[j][k];
    }

    ll ans = 1e18;
    for (int i = 0; i <= N; i++)
        for (int j = 0; j <= N; j++)
            ans = min (ans, dp[i][j]);
    cout << ans << "\n";
}