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 class State {
		int a, b, w;
		public State(int a, int b, int w) {
			this.a = a;
			this.b = b;
			this.w = w;
		}
	}
	
	public static void main(String[] args) throws Exception {
		try(Scanner sc = new Scanner(System.in)) {
			int V = sc.nextInt();
			int E = sc.nextInt();
			int r = sc.nextInt();
			int MAX = 2000001;
			State[] edge = new State[E];
			for(int i=0; i<E; i++) {
				int s = sc.nextInt();
				int t = sc.nextInt();
				int d = sc.nextInt();
				edge[i] = new State(s, t, d);
			}
			int[] dis = new int[V];
			for(int i=0; i<V; i++) {
				dis[i] = MAX;
			}
			dis[r] = 0;
			for(int i=1; ; i++) {
				boolean update = false;
				for(int j=0; j<E; j++) {
					int s = edge[j].a;
					int t = edge[j].b;
					int d = edge[j].w;
					if(dis[s] < MAX && dis[t] > dis[s] + d) {
						dis[t] = dis[s]+d;
						update = true;
					}
				}
				if(i == V && update) {
					System.out.println("NEGATIVE CYCLE");
					return;
				}
				else if(! update) {
					break;
				}
			}
			for(int i=0; i<V; i++) {
				if(dis[i] >= MAX) {
					System.out.println("INF");
				}
				else {
					System.out.println(dis[i]);
				}
			}
		}
	}

}