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 pysnooper
#import numpy
#import os,re,sys,operator
#from collections import Counter,deque
#from operator import itemgetter,mul
#from itertools import accumulate,combinations,groupby,combinations_with_replacement,permutations
from sys import stdin,setrecursionlimit
#from bisect import bisect_left,bisect_right
#from copy import deepcopy
#import heapq
#import math
#import string
#from time import time
#from functools import lru_cache,reduce
#from math import factorial,hypot
#import sys
#from fractions import gcd
setrecursionlimit(10**6)
input=stdin.readline

def main():
    v,e=map(int,input().split())
    INF=2<<31
    d=[[INF]*v for _ in range(v)]
    for _ in range(e):
        s,t,c=map(int,input().split())
        d[s][t]=c
    r=range(v)
    for i in r:d[i][i]=0
    for i in r:
        for j in r:
            for k in r:
                if d[j][i]==INF or d[i][k]==INF:continue
                d[j][k]=min(d[j][k],d[j][i]+d[i][k])

    #for i in d: print(*i)

    for i in r:
        if d[i][i]<0:
            print("NEGATIVE CYCLE")
            exit()

    for i in r:
        for j in r:
            #print(d[i][j],INF,d[i][j]==INF)
            if d[i][j]==INF: d[i][j]="INF"

    for i in d: print(*i)

if __name__=="__main__":main()
