Constraints

* 1 ≤ |V| ≤ 100
* 0 ≤ |E| ≤ 9900
* -2 × 107 ≤ di ≤ 2 × 107
* There are no parallel edges
* There are no self-loops

Input

An edge-weighted graph G (V, E).


|V| |E|
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1


|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

If the graph contains a negative cycle (a cycle whose sum of edge costs is a negative value), print


NEGATIVE CYCLE


in a line.

Otherwise, print


D0,0 D0,1 ... D0,|V|-1
D1,0 D1,1 ... D1,|V|-1
:
D|V|-1,0 D1,1 ... D|V|-1,|V|-1


The output consists of |V| lines. For each ith line, print the cost of the shortest path from vertex i to each vertex j (j = 0, 1, ... |V|-1) respectively. If there is no path from vertex i to vertex j, print "INF". Print a space between the costs.

Examples

Input

4 6
0 1 1
0 2 5
1 2 2
1 3 4
2 3 1
3 2 7


Output

0 1 3 4
INF 0 2 3
INF INF 0 1
INF INF 7 0


Input

4 6
0 1 1
0 2 -5
1 2 2
1 3 4
2 3 1
3 2 7


Output

0 1 -5 -4
INF 0 2 3
INF INF 0 1
INF INF 7 0


Input

4 6
0 1 1
0 2 5
1 2 2
1 3 4
2 3 1
3 2 -7


Output

NEGATIVE CYCLE
#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
#define MAXN 1000+2
long long map1[MAXN][MAXN];
int n,m;
void input(){
	cin>>n>>m;
	int we,xx,yy;
	for(int i=0;i<n;++i){
		for(int j=0;j<n;++j){
			map1[i][j]=10000000000000000;
		}
	}
	for(int i=0;i<n;++i){
		map1[i][i]=0;
	}
	for(int i=0;i<m;++i){
		cin>>xx>>yy>>we;
		map1[xx][yy]=we;
	}
}
void floyd(){
	for(int k=0;k<n;++k){
		for(int i=0;i<n;++i){
			for(int j=0;j<n;++j){
				if(map1[i][k]<10000000000000000&&map1[k][j]<10000000000000000){
				    map1[i][j]=min(map1[i][k]+map1[k][j],map1[i][j]);
				}
			}
		}
	}
	for(int i=0;i<n;++i){
		if(map1[i][i]<0) {
			cout<<"NEGATIVE CYCLE"<<endl;
	        return;
		}
	}
	for(int i=0;i<n;++i){
		for(int j=0;j<n-1;++j){
			if(map1[i][j]<10000000000000000) cout<<map1[i][j]<<" ";
		    else cout<<"INF"<<" ";
		}
		if(map1[i][n-1]<10000000000000000) cout<<map1[i][n-1]<<endl;
	    else cout<<"INF"<<endl;
	}
}
int main(){
	input();
	floyd();
	return 0;
}