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.*;

class Main {
  static final int INF = 2000000000;
  static class Vertex implements Comparable<Vertex> {
    List<Route> routes = new ArrayList<Route>();
    int cost = INF;

    public void addRoute(Vertex to, int dist) {
      routes.add(new Route(this, to, dist));
    }

    public int compareTo(Vertex o) {
      return cost - o.cost;
    }
  }

  static class Route {
    Vertex from;
    Vertex to;
    int weight;

    public Route(Vertex from, Vertex to, int weight) {
      this.from = from;
      this.to = to;
      this.weight = weight;
    }
  }

  public static void main(String[] args) {
    Scanner scan = new Scanner(System.in);
    int v = scan.nextInt();
    int e = scan.nextInt();
    int sP = scan.nextInt();

    Vertex[] vertexArr = new Vertex[v];

    for(int i = 0 ; i < v ; i++) {
      vertexArr[i] = new Vertex();
    }

    int start;
    int end;
    int weight;
    for(int i = 0 ; i < e ; i++) {
      start = scan.nextInt();
      end = scan.nextInt();
      weight = scan.nextInt();
      vertexArr[start].addRoute(vertexArr[end], weight);
    }

    vertexArr[sP].cost = 0;

    PriorityQueue<Vertex> pq = new PriorityQueue<Vertex>(Arrays.asList(vertexArr));
    while (!pq.isEmpty()) {
      Vertex s = pq.poll();
      for (Route route : s.routes) {
        Vertex to = route.to;
        int cost = s.cost + route.weight;
        if (cost < to.cost) {
          pq.remove(to);
          to.cost = cost;
          pq.add(to);
        }
      }
    }

    for (Vertex s : vertexArr) {
      if(s.cost == INF) {
        System.out.println("INF");
      } else System.out.println(s.cost);
    }
  }
}