Problem:
All Pairs Shortest Path

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.

Constraints

1 ≤ |V| ≤ 100

0 ≤ |E| ≤ 9900

-2 × 107 ≤ di ≤ 2 × 107

There are no parallel edges

There are no self-loops

Sample Input 1

4 6
0 1 1
0 2 5
1 2 2
1 3 4
2 3 1
3 2 7

Sample Output 1

0 1 3 4
INF 0 2 3
INF INF 0 1
INF INF 7 0

Sample Input 2

4 6
0 1 1
0 2 -5
1 2 2
1 3 4
2 3 1
3 2 7

Sample Output 2

0 1 -5 -4
INF 0 2 3
INF INF 0 1
INF INF 7 0

Sample Input 3

4 6
0 1 1
0 2 5
1 2 2
1 3 4
2 3 1
3 2 -7

Sample Output 3

NEGATIVE CYCLE

Solution in Ruby (judge verdict: Accepted)

def warshall_floyd(dist)
  # dist: 隣接行列
  #   dist[u][v]はe=(u, v)のコスト(dist[i][i] = 0, 存在しない場合はINF)
  res = dist.dup
  vertex_num = res.size
  vertex_num.times do |k|
    vertex_num.times do |i|
      vertex_num.times do |j|
        res[i][j] = [res[i][j], res[i][k] + res[k][j]].min
      end
    end
  end
  res
end



v, e = gets.split.map(&:to_i)
d = Array.new(v) { Array.new(v, Float::INFINITY) }
v.times { |i| d[i][i] = 0 }
edges = []
e.times do
  s, t, c = gets.split.map(&:to_i)
  d[s][t] = c
  edges << [s, t, c]
  # d[t][s] = c
end
res = warshall_floyd(d)
v.times do |i|
  edges.each do |edge|
    if res[i][edge[0]] + edge[2] < res[i][edge[1]]
      puts "NEGATIVE CYCLE"
      exit
    end
  end
end
res.each do |row|
  puts row.map{|x| x == Float::INFINITY ? "INF" : x} * " "
end