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>

template <class T>
inline void read(T &res)
{
	res = 0; bool bo = 0; char c;
	while (((c = getchar()) < '0' || c > '9') && c != '-');
	if (c == '-') bo = 1; else res = c - 48;
	while ((c = getchar()) >= '0' && c <= '9')
		res = (res << 3) + (res << 1) + (c - 48);
	if (bo) res = ~res + 1;
}

template <class T>
inline T Min(const T &a, const T &b) {return a < b ? a : b;}

typedef long long ll;

const int N = 505;
const ll INF = 1e18;

int n, a[N][N];
ll ans = INF, s1[N][N], s2[N][N], f[N][N];

int main()
{
	read(n);
	for (int i = 1; i <= n; i++) for (int j = 1; j <= n; j++)
		if (i != j) read(a[i][j]);
	for (int i = 1; i <= n; i++) for (int j = 1; j < i; j++)
		s1[i][j] = s1[i][j - 1] + a[j][i], s2[i][j] = s2[i][j - 1] + a[i][j];
	for (int i = 0; i < N; i++) for (int j = 0; j < N; j++)
		f[i][j] = INF; f[1][1] = 0;
	for (int i = 1; i <= n; i++) for (int j = 1; j <= i; j++)
	{
		ll cost = 0;
		for (int k = i + 1; k <= n; k++)
			f[k][i] = Min(f[k][i], f[i][j] + cost + s2[k][i - 1]),
				cost += s2[k][j - 1] + s1[k][k - 1] - s1[k][i - 1];
		ans = Min(ans, f[i][j] + cost);
	}
	return std::cout << ans << std::endl, 0;
}