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<bits/stdc++.h>
using namespace std;


int main(){
  int v,e;cin>>v>>e;
  vector<vector<long long>> dist(v,vector<long long>(v,1e12)) ;
  for (int i = 0; i < v; i++) {
    dist[i][i] = 0;
  }
    
  for (int i = 0; i < e; i++) {
    int s,t,d;cin>>s>>t>>d;
    dist[s][t] = d;
  }

  for (int mid = 0; mid < v; mid++)
  for (int frm = 0; frm < v; frm++) 
  for (int des = 0; des < v; des++) 
  {
    dist[frm][des] = min(dist[frm][des],dist[frm][mid] + dist[mid][des]);
  }

  for (int i = 0; i < v; i++) 
  {
    if(dist[i][i] < 0)
    {
      cout<<"NEGATIVE CYCLE"<< endl;
      return 0;
    }
  }

  for (int i = 0; i < v; i++) 
  {
    if(dist[i][0] <= 1e11)cout << dist[i][0];
    else cout << "INF";
  for (int j = 1; j < v; j++) 
  {
    if(dist[i][j] <= 1e11)cout << " " << dist[i][j];
    else cout << " " << "INF";
  }
  cout << endl;
  }
}

