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
import java.util.Scanner;


public class Main{

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		String[] firstLine = s.nextLine().split(" ");
		int vertexCnt = Integer.parseInt(firstLine[0]);
		int edgeCnt = Integer.parseInt(firstLine[1]);
		int[][] input = new int[vertexCnt][vertexCnt];
		for(int j=0 ; j<vertexCnt ; j++) {
			for(int k=0 ; k<vertexCnt ; k++) {
				if(j==k) {
					input[j][k] = 0;
				}else {
					input[j][k] = Integer.MAX_VALUE;
				}
			}
		}
		for(int i= 0 ; i<edgeCnt ; i++) {
			String[] line = s.nextLine().split(" ");
			input[Integer.parseInt(line[0])][Integer.parseInt(line[1])] = Integer.parseInt(line[2]);
		}
		int[][] result = solve(input);
		for(int l=0 ; l<vertexCnt ; l++) {
			if(result[l][l] < 0) {
				System.out.println("NEGATIVE CYCLE");
				return;
			}
		}
		for(int a=0 ; a<result.length ; a++) {
			String str = "";
			for(int b=0 ; b<result.length ; b++) {
				if(result[a][b]==Integer.MAX_VALUE) {
					str = str + "INF ";
				}else {
					str = str + result[a][b] + " ";
				}
			}
			System.out.println(str.trim());
		}

	}

	public static int[][] solve(int[][] input) {
		int[][] result = new int[input.length][input.length];
		for(int i=0 ; i<input.length ; i++) {
			for(int j=0 ; j<input.length ; j++) {
				for(int k=0 ; k<input.length ; k++) {
					if(input[j][i]!=Integer.MAX_VALUE && input[i][k]!=Integer.MAX_VALUE)
						input[j][k] = Math.min(input[j][k], input[j][i] + input[i][k]);
				}
			}
		}
		return input;
	}

}