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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.io.IOException;
import java.util.ArrayList;
import java.util.Objects;
import java.util.List;
import java.util.AbstractCollection;
import java.io.Closeable;
import java.util.Comparator;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author HBonsai
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ShortestPathDijkstra solver = new ShortestPathDijkstra();
        solver.solve(1, in, out);
        out.close();
    }

    static class ShortestPathDijkstra {
        @SuppressWarnings("unchecked")
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int V = in.nextInt();
            int E = in.nextInt();
            int r = in.nextInt();
            final int INF = Integer.MAX_VALUE;
            List<Edge>[] g = new ArrayList[V]; // suppressしないとここで警告が出る。対処法なし
            Arrays.setAll(g, i -> new ArrayList<>());
            int[] d = new int[V];
            Arrays.fill(d, INF);
            d[r] = 0;
            for (int i = 0; i < E; i++) {
                int v = in.nextInt();
                g[v].add(new Edge(in.nextInt(), in.nextInt()));
            }
            Comparator<Pair> c = Comparator.comparingInt(x -> x.first);
            PriorityQueue<Pair> pairs = new PriorityQueue<>(c);
            pairs.offer(new Pair(0, r));
            while (!pairs.isEmpty()) {
                Pair p = pairs.poll();
                int v = p.second;
                for (int i = 0; i < g[v].size(); i++) {
                    Edge e = g[v].get(i);
                    if (d[e.to] > d[v] + e.cost) {
                        d[e.to] = d[v] + e.cost;
                        pairs.offer(new Pair(d[e.to], e.to));
                    }
                }
            }
            for (int i = 0; i < V; i++) {
                if (d[i] == INF) out.println("INF");
                else out.println(d[i]);
            }

        }

        class Edge {
            public int to;
            public int cost;

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

        }

        class Pair {
            public int first;
            public int second;

            public Pair(int first, int second) {
                this.first = first;
                this.second = second;
            }

            public boolean equals(Object o) {
                if (this == o) return true;
                if (o == null || getClass() != o.getClass()) return false;
                Pair pair = (Pair) o;
                return first == pair.first &&
                        second == pair.second;
            }

            public int hashCode() {
                return Objects.hash(first, second);
            }

        }

    }

    static class FastScanner implements Closeable {
        private final InputStream in;
        private final byte[] buffer = new byte[1024];
        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;
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
            return hasNextByte();
        }

        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 void close() {
            try {
                in.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

    }
}