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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class Main {

	static int d[];
	static int v;

	static List<edge> edges;

	public static void main(String[] args) throws IOException {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		String[] v_e_r = br.readLine().split(" ");

		v = Integer.parseInt(v_e_r[0]);

		int e = Integer.parseInt(v_e_r[1]);

		int r = Integer.parseInt(v_e_r[2]);

		d = new int[v];

		edges = new ArrayList<>();

		for (int i = 0; i < e; i++) {
			String[] from_to_cost_edge = br.readLine().split(" ");

			edges.add(new edge(Integer.parseInt(from_to_cost_edge[0]), Integer.parseInt(from_to_cost_edge[1]),
					Integer.parseInt(from_to_cost_edge[2])));
		}


		if (bellford(r)) {
			System.out.println("NEGATIVE CYCLE");
		} else {

			for (int i = 0; i < d.length; i++) {
				if (d[i] == Integer.MAX_VALUE / 2) {
					System.out.println("INF");
				} else {
					System.out.println(d[i]);
				}
			}
		}

	}

	static boolean judge = false;

	static boolean bellford(int now) {

		Arrays.fill(d, Integer.MAX_VALUE / 2);
		d[now] = 0;
		int i;
		for (i = 0; i < v; i++) {
			for (edge e : edges) {
				if (d[e.from] != Integer.MAX_VALUE/2 && d[e.to] > d[e.from] + e.cost) {
					d[e.to] = d[e.from] + e.cost;

					if (i == v-1) {
						judge = true;
						return true;
					}
				}
				/* System.out.println(e.to+""+e.from); */
			}
		}
		return false;
	}

	static class edge {
		int from;
		int to;
		int cost;

		public edge(int a, int b, int c) {
			this.from = a;
			this.to = b;
			this.cost = c;
		}
	}
}