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.ArrayList;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {
    int n, m, start;
    ArrayList<ArrayList<Edge>> es;

    public static void main(String[] args) {
        Main prob = new Main();
        prob.read();
        prob.solve();
    }

    void read() {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        m = sc.nextInt();
        start = sc.nextInt();
        es = new ArrayList<ArrayList<Edge>>(n);
        for (int i = 0; i < n; i++) {
            es.add(new ArrayList<Edge>());
        }
        for (int i = 0; i < m; i++) {
            int f = sc.nextInt();
            int t = sc.nextInt();
            int c = sc.nextInt();
            es.get(f).add(new Edge(t, c));
        }
    }

    void solve() {
        boolean[] used = new boolean[n];
        int[] dist = new int[n];
        Arrays.fill(dist, Integer.MAX_VALUE);
        int count = 0;
        dist[start] = 0;
        for (int j = 0; j < n; j++) {
            for (int i = 0 ; i < n; i++) {
                for (Edge e: es.get(i)) {
                    if (dist[i] != Integer.MAX_VALUE
                            && dist[e.to] > dist[i] + e.cost) {
                        dist[e.to] = dist[i] + e.cost;
                        if (j == n - 1) {
                            System.out.println("NEGATIVE CYCLE");
                            return;
                        }
                    }
                }
            }
        }

        for (int d: dist) {
            if (d == Integer.MAX_VALUE)
                System.out.println("INF");
            else
                System.out.println(d);
        }
    }

    private class Edge {
        int to, cost;
        Edge(int t, int c) {
            to = t; cost = c;
        }
    }
}