Problem: Constraints

* 1 ≤ |V| ≤ 1000
* 0 ≤ |E| ≤ 2000
* -10000 ≤ di ≤ 10000
* There are no parallel edges
* There are no self-loops

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".

Examples

Input

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


Output

0
2
-3
-1


Input

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


Output

NEGATIVE CYCLE


Input

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


Output

INF
0
-5
-3

Solution (in JAVA):

Solution:

import java.util.*;

public class Main {
	
	static final int INF = Integer.MAX_VALUE/2;
	
	static class Edge{
		int from;
		int to;
		int cost;
		Edge(int from,int to,int cost){
			this.from = from;
			this.to = to;
			this.cost = cost;
		}
	}
	
	public static void main(String[] args){
		Scanner stdIn = new Scanner(System.in);
		int V = stdIn.nextInt();
		int E = stdIn.nextInt();
		int r = stdIn.nextInt();
		
		int[] d = new int[V];
		Arrays.fill(d,INF);
		d[r] = 0;
		
		ArrayList<Edge> list = new ArrayList<Edge>();
		for(int i=0;i<E;i++){
			int s = stdIn.nextInt();
			int t = stdIn.nextInt();
			int l = stdIn.nextInt();
			Edge edge = new Edge(s,t,l);
			list.add(edge);
		}
		
		for(int i=0;i<V;i++){
			for(int j=0;j<E;j++){
				Edge edge = list.get(j);
				if(d[edge.from]!=INF && d[edge.to]>d[edge.from]+edge.cost){
					d[edge.to] = d[edge.from]+edge.cost;
					if(i==V-1){
						System.out.println("NEGATIVE CYCLE");
						return;
					}
				}
			}
		}
		
		for(int i=0;i<V;i++){
			if(d[i]>INF/2){
				System.out.println("INF");
			}
			else{
				System.out.println(d[i]);
			}
		}
	}
}