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.Arrays;
import java.util.Scanner;

public class Main{

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int v = sc.nextInt();
        int e = sc.nextInt();
        int s = sc.nextInt();
        int[][] edge = new int[e][3];
        for (int i = 0; i < e; i++) {
            edge[i][0] = sc.nextInt();
            edge[i][1] = sc.nextInt();
            edge[i][2] = sc.nextInt();
        }
        long[] ans = bellmanFord(v, edge, s);
        if(ans == null) System.out.println("NEGATIVE CYCLE");
        else for(long a : ans){
            if(a == Long.MAX_VALUE) System.out.println("INF");
            else System.out.println(a);
        }

        sc.close();

    }
    public static long[] bellmanFord(int n, int[][] edge, int s){
        long d[] = new long[n];
        Arrays.fill(d, Long.MAX_VALUE);
        d[s] = 0;
        for (int i = 0; i < n; i++) {
            for(int j = 0; j < edge.length; j++){
                int[] e = edge[j];
                if(d[e[0]] != Long.MAX_VALUE && d[e[1]] > d[e[0]] + e[2]){
                    d[e[1]] = d[e[0]] + e[2];
                    if(i == n - 1){
                        d = null;
                        break;
                    }
                }
            }
        }
        return d;
    }

}