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: Runtime Error)

class Node
  attr_accessor :name, :child, :done, :cost
  def initialize(i)
    @name = i
    @child = {}
    @done = false
    @cost = 1.0 / 0.0
  end
end

v, e, r = gets.split.map(&:to_i)

node = Array.new(v){|i| Node.new(i)}
e.times{
  s, t, d = gets.split.map(&:to_i)
  node[s].child[t] = d
}

node[r].cost = 0

(v-1).times{|i|
  v.times{|j|
    node[j].child.each{|t,d|
      if node[t].cost > node[j].cost + d then
        node[t].cost = node[j].cost + d
      end
    }
  }
}

v.times{|j|
  node[j].child.each{|t,d|
    if node[j].cost + d < node[t].cost then
      puts "NEGATIVE CYCLE"
      exit
    end
  }
  node[j].cost = "INF" if node[j].cost == 1.0 / 0.0
}

v.times{|j|
  puts node[j].cost
}