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 sys
import math
import fractions
import itertools
from collections import deque
import copy
import heapq
import bisect

MOD = float('inf')
INF = 10 ** 18 + 7
input = lambda: sys.stdin.readline().strip()


def warshall_floyd(d):
    """
    d[i][l]がi→lへのコストを示す隣接行列
    結果としてd[i][l]はi→lへの最短コストになる。
    """
    for i in range(len(d)):
        for l in range(len(d)):
            for k in range(len(d)):
                d[l][k] = min(d[l][k], d[l][i] + d[i][k])
    return d


V, E = map(int, input().split())
std = [list(map(int, input().split())) for _ in range(E)]
d = [[INF for _ in range(V)] for _ in range(V)]
for i in range(V):
    d[i][i] = 0
for i in std:
    d[i[0]][i[1]] = i[2]

ans = warshall_floyd(d)
for i in range(V):
    if ans[i][i] < 0:
        print("NEGATIVE CYCLE")
        sys.exit()
for i in range(V):
    for l in range(V):
        if ans[i][l] > 10 ** 11:
            ans[i][l] = "INF"
        else:
            ans[i][l] = str(ans[i][l])

for i in ans:
    print(" ".join(i))

