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.IOException;
import java.io.InputStream;
import java.util.*;

class Edge {
    int from, to, cost;

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

public class Main {

    static int V, E, r;
    static List<List<Edge>> graph;
    static double[] dist;

    static boolean bellmanFord() {
        dist = new double[V];
        Arrays.fill(dist, Double.POSITIVE_INFINITY);
        dist[r] = 0;

        for (int i = 0; i < V -1; ++i) {
            for (List<Edge> edges : graph) {
                for (Edge e : edges) {
                    if (dist[e.to] > dist[e.from] + e.cost) {
                        dist[e.to] = dist[e.from] + e.cost;
                    }
                }
            }
        }

        for (int i = 0; i < V -1; ++i) {
            for (List<Edge> edges : graph) {
                for (Edge e : edges) {
                    if (dist[e.to] > dist[e.from] + e.cost) {
                        return false;
                    }
                }
            }
        }

        return true;
    }

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        V = fs.nextInt();
        E = fs.nextInt();
        r = fs.nextInt();
        graph = new ArrayList<>();
        for (int i = 0; i < V; ++i) graph.add(new ArrayList<>());
        for (int i = 0; i < E; ++i) {
            int from = fs.nextInt();
            int to = fs.nextInt();
            int cost = fs.nextInt();
            graph.get(from).add(new Edge(from, to, cost));
        }

        if (bellmanFord()) {
            for (int i = 0; i < V; ++i) {
                if (dist[i] == Double.POSITIVE_INFINITY)
                    System.out.println("INF");
                else
                    System.out.println((int)dist[i]);
            }
        } else {
            System.out.println("NEGATIVE CYCLE");
        }
    }
}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}

    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }

    public double nextDouble() { return Double.parseDouble(next());}
}