Problem: For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Constraints

* 1 ≤ |V| ≤ 100000
* 0 ≤ di ≤ 10000
* 0 ≤ |E| ≤ 500000
* 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

Print the costs of SSSP in the following format.


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 1
0 2 4
1 2 2
2 3 1
1 3 5


Output

0
1
3
4


Input

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5


Output

3
0
2
INF

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {
    private HashMap<Integer, List<Edge>> graph;

    public static void main(String[] args) throws Exception {
        new Main().solve();
    }

    private void solve() throws Exception{
        FastScanner scanner = new FastScanner(System.in);

        int V = scanner.nextInt();
        int E = scanner.nextInt();
        int src = scanner.nextInt();

        graph = new HashMap<>(V);
        for(int i = 0; i < V; ++i){
            graph.put(i, new ArrayList<Edge>());
        }

        for(int i = 0; i < E; ++i){
            int u = scanner.nextInt();
            int v = scanner.nextInt();
            int w = scanner.nextInt();

            graph.get(u).add(new Edge(v, w));
        }

        int[] dist = new int[V];
        Arrays.fill(dist, Integer.MAX_VALUE);
        dist[src] = 0;
        PriorityQueue<Edge> queue = new PriorityQueue<Edge>(11, new Comparator<Edge>() {
            @Override
            public int compare(Edge o1, Edge o2) {
                return o1.weight - o2.weight;
            }
        });

        queue.offer(new Edge(src, 0));
        boolean[] visited = new boolean[V];

        while(!queue.isEmpty()){
            Edge edge = queue.poll();
            int u = edge.v;
            if(visited[u]){
                continue;
            }
            visited[u] = true;

            for(Edge adj : graph.get(u)){
                int v = adj.v;
                if(dist[v] > dist[u] + adj.weight){
                    dist[v] = dist[u] + adj.weight;
                    adj.weight = dist[v];
                    queue.offer(adj);
                }
            }
        }

        PrintWriter printWriter = new PrintWriter(System.out);
        for(int i = 0; i < V; ++i){
            if(dist[i] == Integer.MAX_VALUE){
                printWriter.println("INF");
            }
            else{
                printWriter.println(dist[i]);
            }
        }
        printWriter.flush();
    }

    static class Edge{
        int v;
        int weight;

        public Edge(int v, int weight){
            this.v = v;
            this.weight = weight;
        }
    }

    static class FastScanner {
        private InputStream in;
        private final byte[] buffer = new byte[1024 * 8];
        private int ptr = 0;
        private int buflen = 0;

        public FastScanner(InputStream in){
            this.in = in;
        }

        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;
        }

        private void skipUnprintable() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
        }

        public boolean hasNext() {
            skipUnprintable();
            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() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

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