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.*;
 
class Main {
    public static void main(String[] args) throws IOException {
        InputStreamReader isr = new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(isr);
        String[] line1 = br.readLine().split(" ");
        int V = Integer.valueOf(line1[0]);
        int E = Integer.valueOf(line1[1]);
        int r = Integer.valueOf(line1[2]);
        List<List<Edge>> list = new ArrayList<List<Edge>>();
        for (int i = 0; i < V; i++) {
            list.add(i, new ArrayList<Edge>());
        }
 
        for (int i = 0; i < E; i++) {
            String[] line = br.readLine().split(" ");
            int s = Integer.valueOf(line[0]);
            int t = Integer.valueOf(line[1]);
            int d = Integer.valueOf(line[2]);
            Edge edge = new Edge(t, d);
            list.get(s).add(edge);
        }
 
        int[] dist = new int[V];
        Arrays.fill(dist, 20000000);
        dist[r] = 0;
        for (int i = 0; i < V - 1; i++) {
            for (int j = 0; j < V; j++) {
                if (dist[j] != 20000000) {
                    for (int k = 0; k < list.get(j).size(); k++) {
                        Edge edge = (Edge) (list.get(j).get(k));
                        dist[edge.to] = Math.min(dist[edge.to], dist[j] + edge.dist);
                    }
                }
 
            }
        }
        //最後
        for (int j = 0; j < V; j++) {
            if (dist[j] != 20000000) {
                for (int k = 0; k < list.get(j).size(); k++) {
                    Edge edge = (Edge) (list.get(j).get(k));
                    if (dist[edge.to] > dist[j] + edge.dist) {
                        System.out.println("NEGATIVE CYCLE");
                        return;
                    }
                }
            }
        }
        for (int i = 0; i < V; i++) {
            if (dist[i] == 20000000) {
                System.out.println("INF");
            } else {
                System.out.println(dist[i]);
            }
        }
    }
 
}
 
class Edge {
 
    int to, dist;
 
    public Edge(int to, int dist) {
        this.to = to;
        this.dist = dist;
    }
}