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.Arrays;

public class Main {

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

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] str = br.readLine().split(" ");
        int v = Integer.parseInt(str[0]);
        int e = Integer.parseInt(str[1]);
        int r = Integer.parseInt(str[2]);

        edge[] es = new edge[e];
        for (int i = 0; i < e; i++) {
            str = br.readLine().split(" ");
            edge ed = new edge();
            ed.from = Integer.parseInt(str[0]);
            ed.to = Integer.parseInt(str[1]);
            ed.cost = Integer.parseInt(str[2]);

            es[i] = ed;
        }

        long[] distance = new long[v];
        Arrays.fill(distance, Long.MAX_VALUE);
        distance[r] = 0;
        for (int i = 0; i < v; i++) {
            for (int j = 0; j < e; j++) {
                edge ed = es[j];
                if (distance[ed.from] != Long.MAX_VALUE)
                    distance[ed.to] = Long.min(distance[ed.to], distance[ed.from] + ed.cost);
            }
        }

        boolean update = false;
        for (int i = 0; i < v; i++) {
            for (int j = 0; j < e; j++) {
                edge ed = es[j];
                if (distance[ed.from] != Long.MAX_VALUE) {
                    if(distance[ed.to] > distance[ed.from] + ed.cost){
                        distance[ed.to] = distance[ed.from] + ed.cost;
                        update = true;
                    }
                }
            }
            if (update) break;
        }

        if (update) {
            System.out.println("NEGATIVE CYCLE");
        } else {
            for (int i = 0; i < distance.length; i++) {
                if (distance[i] == Long.MAX_VALUE) {
                    System.out.println("INF");
                } else {
                    System.out.println(distance[i]);
                }
            }
        }
    }
}