Problem:
Single Source Shortest Path (Negative Edges)

Input

An edge-weighted graph G (V, E) and the source r.

|V| |E| r
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. r is the source of the graph.

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) which is reachable from the source r, print

NEGATIVE CYCLE

in a line.

Otherwise, print

c0
c1
:
c|V|-1

The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print "INF".

Constraints

1 ≤ |V| ≤ 1000

0 ≤ |E| ≤ 2000

-10000 ≤ di ≤ 10000

There are no parallel edges

There are no self-loops

Sample Input 1

4 5 0
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2

Sample Output 1

0
2
-3
-1

Sample Input 2

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

Sample Output 2

NEGATIVE CYCLE

Sample Input 3

4 5 1
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2

Sample Output 3

INF
0
-5
-3

Solution in Ruby (judge verdict: Accepted)

n, m, r = gets.split.map(&:to_i)
g = (0..n-1).map { {} }
m.times do
  i, j, c = gets.split.map(&:to_i)
  g[i][j] = c
end

dist = Hash.new(Float::INFINITY)
dist[r] = 0
(n - 1).times do
  (0..n-1).each do |i|
    g[i].each do |j, c|
      dist[j] = [dist[j], dist[i] + c].min
    end
  end
end

has_negative_cycle = false
catch :exit do
  (0..n-1).each do |i|
    g[i].each do |j, c|
      if dist[i] + c < dist[j]
        has_negative_cycle = true
        throw :exit
      end
    end
  end
end

if has_negative_cycle
  puts 'NEGATIVE CYCLE'
else
  (0..n-1).each do |i|
    puts dist[i] == Float::INFINITY ? 'INF' : dist[i]
  end
end