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.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    void solve() throws IOException {
        int v = ni(), e = ni(), r = ni();

        ArrayList<ArrayList<Edge>> G = new ArrayList<>();
        for (int i = 0; i < v; i++) {
            G.add(new ArrayList<>());
        }

        for (int i = 0; i < e; i++) {
            int s = ni(), t = ni(), d = ni();
            G.get(s).add(new Edge(t, d));
        }

        BellmanFord bel = new BellmanFord(G);
        int[] dist = bel.getDist(r);

        if (dist == null) {
            out.println("NEGATIVE CYCLE");
            return;
        }

        int INF = Integer.MAX_VALUE / 3;

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

    class BellmanFord {
        int n;
        java.util.ArrayList<java.util.ArrayList<Edge>> G;

        int INF = Integer.MAX_VALUE / 3;

        BellmanFord(java.util.ArrayList<java.util.ArrayList<Edge>> G) {
            n = G.size();
            this.G = G;
        }

        int[] getDist(int s) {
            int[] dist = new int[n];
            Arrays.fill(dist, INF);
            dist[s] = 0;
            for (int i = 0; i < n; i++) {
                boolean update = false;
                for (int j = 0; j < n; j++) {
                    for (Edge e : G.get(j)) {
                        if (dist[j] != INF && dist[e.to] > dist[j] + e.cost) {
                            if (i == n - 1) return null;

                            dist[e.to] = dist[j] + e.cost;
                            update = true;
                        }
                    }
                }
                if (!update) break;
            }
            return dist;
        }
    }

    class Edge implements Comparable<Edge> {
        int to;
        int cost;

        Edge(int to, int cost) {
            this.to = to;
            this.cost = cost;
        }

        public int compareTo(Edge edge) {
            return cost - edge.cost;
        }
    }

    String ns() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine(), " ");
        }
        return tok.nextToken();
    }

    int ni() throws IOException {
        return Integer.parseInt(ns());
    }

    long nl() throws IOException {
        return Long.parseLong(ns());
    }

    double nd() throws IOException {
        return Double.parseDouble(ns());
    }

    String[] nsa(int n) throws IOException {
        String[] res = new String[n];
        for (int i = 0; i < n; i++) {
            res[i] = ns();
        }
        return res;
    }

    int[] nia(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = ni();
        }
        return res;
    }

    long[] nla(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = nl();
        }
        return res;
    }

    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        tok = new StringTokenizer("");
        Main main = new Main();
        main.solve();
        out.close();
    }
}