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 {
	public static void main(String[] args) {
		try(Scanner sc = new Scanner(System.in)){
			int v=sc.nextInt();
			int e=sc.nextInt();
			int r=sc.nextInt();
			int INF=100000000;
			int[] s=new int[e];
			int[] t=new int[e];
			int[] cost=new int[e];
			for(int i=0; i<e; i++) {
				s[i]=sc.nextInt();
				t[i]=sc.nextInt();
				cost[i]=sc.nextInt();
			}
			int[] d=new int[v];
			for(int i=0; i<v; i++) {
				d[i]=INF;
			}
			d[r]=0;
			int count=0;
			int end=1;
			for(int k=0; k<v; k++) {
				count++;
				//System.out.println("k="+k);
				boolean update=false;
				for(int i=0; i<e; i++) {
					if(d[s[i]]<INF && d[t[i]]>d[s[i]]+cost[i]) {
						if(count==v) {
							end=0;
							break;
						}
						d[t[i]]=d[s[i]]+cost[i];
						update=true;
					}
					//System.out.println("d["+t[i]+"]="+d[t[i]]);
				}
				if(! update) {
					break;
				}
				if(end==0) {
					break;
				}
			}
			if(end==0) {
				System.out.println("NEGATIVE CYCLE");
			}
			else {
				for(int i=0; i<v; i++) {
					if(d[i]==INF) System.out.println("INF");
					else System.out.println(d[i]);
				}
			}
			
		}
	}
}