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.*;

class Main {
    //Bellman-Ford's Algorithm
    private static final int MAX = 99999;
    public static void main(String[] args) throws Exception {
        Scanner scanner = new Scanner(System.in);
        int V = scanner.nextInt();
        int E = scanner.nextInt();
        int src = scanner.nextInt();

        int[] dist = new int[V];
        int[][] edges = new int[E][3];

        for(int i = 0; i < V; ++i){
            dist[i] = MAX;
        }
        dist[src] = 0;

        for(int i = 0; i < E; ++i){
            int[] edge = new int[] {scanner.nextInt(), scanner.nextInt(), scanner.nextInt()};
            edges[i] = edge;
        }

        for(int i = 1; i < V; ++i){
            for(int j = 0; j < E; ++j){
                int[] edge = edges[j];
                if(dist[edge[0]] != MAX && dist[edge[1]] > dist[edge[0]] + edge[2]){
                    dist[edge[1]] = dist[edge[0]] + edge[2];
                }
            }
        }

        boolean containNegativeCycle = false;
        for(int j = 0; j < E; ++j){
            int[] edge = edges[j];
            if(dist[edge[0]] != MAX && dist[edge[1]] > dist[edge[0]] + edge[2]){
                containNegativeCycle = true;
                break;
            }
        }

        if(containNegativeCycle){
            System.out.println("NEGATIVE CYCLE");
            return;
        }

        for(int i = 0; i < V; ++i){
            System.out.println(dist[i] == MAX ? "INF" : dist[i]);
        }
    }
}