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.PriorityQueue;
import java.util.Scanner;

/**
 * Created by shoya on 2017/04/12.
 */
public class Main {
    public static void main(String... args) {
        Scanner sc = new Scanner(System.in);
        int V = sc.nextInt();
        int E = sc.nextInt();
        int r = sc.nextInt();
        DijkstraClass dijkstra = new DijkstraClass(V, E, r);
        for (int i = 0; i < E; i++) {
            int s = sc.nextInt();
            int d = sc.nextInt();
            int c = sc.nextInt();
            dijkstra.addDistande(s, d, c);
        }
        int[] dist = dijkstra.dikstra();
        for (int i = 0; i < dist.length; i++){
            if (dist[i] == 1 << 30)
                System.out.println("INF");
            else
                System.out.println(dist[i]);
        }
        return;
    }


    private static class DijkstraClass {
        class edge{
            int dest, cost;
            edge(int dest, int cost){
                this.dest = dest;
                this.cost = cost;
            }
        }

        private final int INF = 1 << 30;
        private int S;
        private int V;
        private ArrayList<ArrayList<edge>> edgesOfNodes = new ArrayList<ArrayList<edge>>();

        DijkstraClass(int V, int E, int Start){
            this.S = Start;
            this.V = V;
            for (int i = 0; i < V; i++)
                edgesOfNodes.add(new ArrayList<edge>());
        }

        void addDistande(int source, int dest, int cost){
            edgesOfNodes.get(source).add(new edge(dest, cost));
        }


        int[] dikstra(){
            class costAndNode implements Comparable {
                int cost, node;
                costAndNode(int cost, int node){
                    this.cost = cost;
                    this.node = node;
                }
                @Override
                public int compareTo(Object o) {
                    return this.cost - ((costAndNode) o).cost;
                }
            }

            PriorityQueue<costAndNode> pque = new PriorityQueue<costAndNode>();
            int[] distances = new int[V];
            for (int i = 0; i < V; i++)
                distances[i] = INF;
            distances[S] = 0;

            pque.add(new costAndNode(0, S));
            while (!pque.isEmpty()){
                costAndNode item = pque.poll();
                if (distances[item.node] < item.cost)
                    continue;

                //System.out.printf("Focusing on Node %d\n", item.node);
                //for (int i = 0; i < V; i++)
                //    System.out.printf("%d ", distances[i]);
                //System.out.println();

                for (edge e : edgesOfNodes.get(item.node)) {
                    //System.out.printf("Node %d -> %d, Cost %d -> %d\n",
                    //        item.node, e.dest, distances[e.dest],
                    //        distances[item.node] + e.cost);
                    if (distances[e.dest] > distances[item.node] + e.cost) {
                        distances[e.dest] = distances[item.node] + e.cost;
                        pque.add(new costAndNode(distances[e.dest], e.dest));
                    }
                }
            }

            return distances;
        }

    }
}