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.Scanner;

public class Main{
	static final int MAX = 1000;
	static final int INF = 1 << 21;
	static final int WHITE = 0;
	static final int GRAY = 1;
	static final int BLACK = 2;
	static int n, r, q;
	static Edge[]e;
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
	    n = scan.nextInt();
	    q = scan.nextInt();
	    e = new Edge[q];
	    r = scan.nextInt();	// 始点
	    for(int i = 0; i < q; i++) {
	    	int s = scan.nextInt();
	    	int t = scan.nextInt();
	    	int d = scan.nextInt();
	    	e[i] = new Edge(s, t, d);
	    }
	    scan.close();
	    //bellmanFord();
	    if(bellmanFord()) {
	    	System.out.println("NEGATIVE CYCLE");
	    }else {
	    	for(int i = 0; i < n; i++) {
		    	if(d[i] == INF) {
		    		System.out.println("INF");
		    	}else {
		    		System.out.println(d[i]);
		    	}
		    }
	    }


	}
    static int[]d = new int[MAX];
	static boolean bellmanFord() {
        for(int i = 0; i < n; i++) {
            d[i] = INF;
        }
        d[r] = 0;
        for(int i = 0; i < n; i++) {
        	for(int j = 0; j < q; j++) {
        		if(d[e[j].from] != INF && d[e[j].to] > d[e[j].from] + e[j].cost) {
        			d[e[j].to] = d[e[j].from] + e[j].cost;
        			if(i == n - 1) return true;
        		}
        	}
        }
        return false;
	}
	static class Edge{
		int from, to, cost;
		public Edge(int from, int to, int cost) {
			this.from = from;
			this.to= to;
			this.cost = cost;
		}
	}
}