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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int V = Integer.parseInt(sc.next());
        int E = Integer.parseInt(sc.next());
        int r = Integer.parseInt(sc.next()); // root
        long INF = 200_000_000_000_000_000L;
        ArrayList<int[]> edge = new ArrayList<int[]>();
        for (int i=0;i<E;i++) {
            int s = Integer.parseInt(sc.next());
            int t = Integer.parseInt(sc.next());
            int d = Integer.parseInt(sc.next());
            int[] add = {s, t, d};
            edge.add(add);
        }

        long[] values = new long[V];
        for (int i=0;i<V;i++) {
            if (i!=r) {
                values[i]=INF;
            }
        }
        int flag = 0;
        for (int k=0;k<V;k++) {
            for (int i=0;i<E;i++) {
                    int[] tmp = edge.get(i);
                    if ((values[tmp[0]] != INF) && (values[tmp[1]] > values[tmp[0]]+tmp[2])) {
                        values[tmp[1]] = values[tmp[0]]+tmp[2];
                        if (k==V-1) {
                            flag=1;
                        }
                    }
            }
        }

        if (flag==1) {
            System.out.println("NEGATIVE CYCLE");
        } else {
            for (int i=0;i<V;i++) {
                if (values[i]==INF) {
                    System.out.println("INF");
                } else {
                    System.out.println(values[i]);
                }
            }
        }
    }
}