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.util.ArrayList;
import java.util.Comparator;
import java.util.HashSet;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {

    public static class DijkstraShortestPath {

        Integer[] shortestPaths; // index is vertex

        public DijkstraShortestPath(WeightedDigraph graph, int sourceVertex) {
            shortestPaths = new Integer[graph.numVertex];
            shortestPaths[sourceVertex] = 0;
            MinPriorityQ<PathWithV> minPQ = new MinPriorityQ<PathWithV>(new Comparator<PathWithV>() {
                @Override
                public int compare(PathWithV o1, PathWithV o2) {
                    return o1.path - o2.path;
                }
            });
            PathWithV p = new PathWithV(sourceVertex, 0);
            minPQ.add(p);
            while (!minPQ.isEmpty()) {
                p = minPQ.remove();
                int vertex = p.vertex;

                for (WeightedDigraph.Edge edge : graph.srcEdges[vertex]) {
                    Integer targetVertexPath = shortestPaths[edge.targetVertex];
                    if (targetVertexPath == null || shortestPaths[vertex] + edge.weight < targetVertexPath) {
                        shortestPaths[edge.targetVertex] = shortestPaths[vertex] + edge.weight;
                        p = new PathWithV(edge.targetVertex, shortestPaths[edge.targetVertex]);
                        minPQ.addOrUpdateKey(p);
                    }
                }
            }
        }

        class PathWithV {

            int path;
            int vertex;

            public PathWithV(int vertex, int path) {
                this.path = path;
                this.vertex = vertex;
            }

            @Override
            public boolean equals(Object obj) {
                if (obj instanceof PathWithV) {
                    final PathWithV other = (PathWithV) obj;
                    if (this.vertex != other.vertex) {
                        return false;
                    }
                }

                return false;
            }

        }

        /**
         *
         * @param vertex
         * @return null meaning INF
         */
        public Integer shortestPath(int vertex) {
            return shortestPaths[vertex];
        }
    }

    public static class WeightedDigraph {

        int numVertex;
        int numEdge;

        List<Edge> edges = new ArrayList<>();
        List<Edge>[] srcEdges;

        @SuppressWarnings("unchecked")
        public WeightedDigraph(int numV, int numE) {
            this.numVertex = numV;
            this.numEdge = numE;
            srcEdges = new List[numV];

            for (int i = 0; i < numV; i++) {
                srcEdges[i] = new ArrayList<Edge>();
            }
        }

        public void addEdge(int srcVertex, int targetVertex, int weight) {
            Edge e = new WeightedDigraph.Edge(srcVertex, targetVertex, weight);
            edges.add(e);
            srcEdges[srcVertex].add(e);
        }

        public static class Edge {

            int srcVertex;
            int targetVertex;
            int weight;

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

    }

    /**
     * Mimic raise key value by introducing a HashSet lookup.
     */
    public static class MinPriorityQ<E> extends PriorityQueue<E> {

        public MinPriorityQ(Comparator<? super E> comparator) {
            super(comparator);
        }
        HashSet<E> set = new HashSet<E>();

        public boolean add(E e) {
            set.add(e);
            return super.add(e);
        }

        public void addOrUpdateKey(E e) {
            if (set.contains(e)) {
                super.remove(e);
                add(e);
            } else {
                set.add(e);
                add(e);
            }
        }
        
        public boolean remove(Object o) {
            if (set.remove(o)) {
                return super.remove(o);
            }
            return false;
        }
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int numVertex = scanner.nextInt();
        int numEdge = scanner.nextInt();
        WeightedDigraph graph = new WeightedDigraph(numVertex, numEdge);
        int srcVertex = scanner.nextInt();
        while (numEdge-- > 0) {
            int srcV = scanner.nextInt();
            int targetV = scanner.nextInt();
            int weight = scanner.nextInt();
            graph.addEdge(srcV, targetV, weight);
        }

        DijkstraShortestPath dijkstra = new DijkstraShortestPath(graph, srcVertex);
        for (int i = 0; i < graph.numVertex; i++) {
            Integer v = dijkstra.shortestPath(i);
            System.out.println(v == null ? "INF" : v);
        }
    }
}