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
readline = sys.stdin.readline
writelines = sys.stdout.writelines
write = sys.stdout.write

from collections import deque
from heapq import heappush, heappop

INF = 10**30
def Johnson(G):
    h = [0]*N

    update = 1
    for i in range(N):
        update = 0
        for v in range(N):
            d = h[v]
            for w, c in G[v]:
                if c + d < h[w]:
                    h[w] = d + c
                    update = 1
        if not update:
            break
    else:
        return None

    for v in range(N):
        d = h[v]
        g = G[v]
        for j, (w, c) in enumerate(g):
            g[j] = (w, c + d - h[w])

    D = []
    for i in range(N):
        dst = [INF]*N
        dst[i] = 0
        que = [(0, i)]
        while que:
            cost, v = heappop(que)
            if dst[v] < cost:
                continue
            for w, c in G[v]:
                if cost + c < dst[w]:
                    dst[w] = r = cost + c
                    heappush(que, (r, w))
        v = h[i]
        for j in range(N):
            if dst[j] == INF:
                dst[j] = INF
            else:
                dst[j] -= v - h[j]
        D.append(dst)

    return D


N, M = map(int, input().split())
G = [[] for i in range(N)]
for i in range(M):
    s, t, d = map(int, input().split())
    G[s].append((t, d))

D = Johnson(G)
if D:
    ans = []
    for i in range(N):
        ans.append(" ".join(str(v) if v < INF else "INF" for v in D[i]))
        ans.append("\n")
    writelines(ans)
else:
    write("NEGATIVE CYCLE\n")

