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>
#define meow(args...) fprintf(stderr, args)
template<class T1, class T2> inline bool cmin(T1 &a, const T2 &b) {return b<a?(a=b, true):false;}
template<class T1, class T2> inline bool cmax(T1 &a, const T2 &b) {return a<b?(a=b, true):false;}
template<class Type> Type read() {
	Type a;
	bool b;
	unsigned char c;
	while(c=getchar()-48, (c>9)&(c!=253));
	for(a=(b=c==253)?0:c; (c=getchar()-48)<=9; a=a*10+c);
	return b?-a:a;
}
auto rd=read<int>;
typedef unsigned u32;
typedef long long s64;
typedef unsigned long long u64;

const int N=501;
int n, a[N][N];
s64 s[N][N], ds[N][N], f[N][N];
int main() {
	n=rd();
	for(int i=1; i<=n; ++i) {
		for(int j=1; j<=n; ++j) if(i!=j) a[i][j]=rd();
		for(int j=1; j<=n; ++j) s[i][j]=s[i][j-1]+a[i][j];
		for(int j=1; j<=n; ++j) s[i][j]+=s[i-1][j];
		for(int j=i; j<=n; ++j) ds[i][j]=ds[i][j-1]+a[i][j];
		for(int j=1; j<=n; ++j) ds[i][j]+=ds[i-1][j];
	}
	for(int i=0; i<=n; ++i) memset(f[i], 63, (n+1)*sizeof(s64));
	f[0][0]=0;
	for(int i=0; i<=n; ++i)
		for(int j=i; j<=n; ++j)
			if(f[i][j]<1e18)
				for(int k=j+1; k<=n; ++k)
					cmin(f[j][k], f[i][j]+ds[k][k]-ds[j][k]-ds[k][j]+ds[j][j]+s[k][i]-s[j][i]);
	s64 ans=1e18;
	for(int i=1; i<n; ++i) cmin(ans, f[i][n]);
	printf("%llu\n", ans);
	return 0;
}
