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 {
	static final int MAX = 100;
	static final long INF = (1L << 32);
	static int n;
	static long[][]d = new long[MAX][MAX];
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		n = scan.nextInt();
		int q = scan.nextInt();
		for(int i = 0; i < n; i++) {
			for(int j = 0; j < n; j++) {
				if(i != j) d[i][j] = INF;
			}
		}
		for(int i = 0; i < q; i++) {
			int u = scan.nextInt();
			int v = scan.nextInt();
			int c = scan.nextInt();
			d[u][v] = c;
		}
		scan.close();
		warshallFloyd();
		boolean negative = false;
		for(int i = 0; i < n; i++){
			if(d[i][i] < 0) negative = true;
		}
		if(negative) {
			System.out.println("NEGATIVE CYCLE");
		}else {
			for(int i = 0; i < n; i++) {
				for(int j = 0; j < n; j++) {
					if(j == n - 1) {
						if(d[i][j] == INF) System.out.println("INF");
						else System.out.println(d[i][j]);
					}
					else {
						if(d[i][j] == INF) System.out.print("INF ");
						else System.out.print(d[i][j] + " ");
					}
				}
			}
		}
	}
	static void warshallFloyd() {
		for(int k = 0; k < n; k++) {
			for(int i = 0; i < n; i++) {
				if(d[i][k] == INF) continue;
				for(int j = 0; j < n; j++) {
					if(d[k][j] == INF) continue;
					d[i][j] = Math.min(d[i][j], d[i][k] + d[k][j]);
				}
			}
		}
	}
}
