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.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;


public class Main{

	@SuppressWarnings("unchecked")
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int V = in.nextInt();
		int E = in.nextInt();
		int r = in.nextInt();
		
		lEdge = new List[V];
		for (int i=0;i<V;i++) {
			lEdge[i] = new ArrayList<P>();
		}
		for (int i=0;i<E;i++) {
			lEdge[in.nextInt()].add(new P(in.nextInt(), in.nextDouble()));
		}
		dist = new double[V];
		Arrays.fill(dist, Double.MAX_VALUE);
		
		if(bellmanFord(r)) {
			System.out.println("NEGATIVE CYCLE");
		} else {
			for (int i=0;i<dist.length;i++) {
				System.out.println(dist[i]==Double.MAX_VALUE ? "INF" : (int)dist[i]);
			}
		}
	}

	static List<P>[] lEdge;
	static double[] dist;

	static boolean bellmanFord(int s) { // s is start
		dist[s] = 0.0;
		int nLoop = 0;
		while (true) {
			boolean bUpdate = false;
			for (int i=0;i<lEdge.length;i++) {
				int from = i;
				if (dist[from]==Double.MAX_VALUE) continue;
				for (P p : lEdge[i]) {
					int to = p.index;
					if (dist[to] > dist[from] + p.length) {
						dist[to] = dist[from] + p.length;
						bUpdate = true;
					}
				}
			}
			if (bUpdate && nLoop==lEdge.length) return true; // has negative loop
			nLoop++;
			if (!bUpdate) break;
		}
		return false; // has no negative loop
	}

	static class P implements Comparable<P> {
		int index; double length;
		public P(int index, double length) {this.index = index; this.length = length;}
		public int compareTo(P p) {return this.length < p.length ? -1 : this.length == p.length ? 0 : 1;}
		public String toString() {return index+","+length;}
	}
}