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:
// GRL_1_A: SSSP, nonnegative edges (Dijkstra's)

import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int m = sc.nextInt();
    int source = sc.nextInt();

    Map<Integer, Integer> cost = new HashMap<Integer, Integer>();
    cost.put(source, 0);

    // representing vertices as int[] with values {id, tentative cost}
    PriorityQueue<int[]> pq =
        new PriorityQueue<int[]>(
            new Comparator<int[]>() {
              public int compare(int[] v1, int[] v2) {
                return Integer.compare(v1[1], v2[1]);
              }
            });

    // populate adjacency list
    // adj[i] = list of all edges from node i
    ArrayList<ArrayList<int[]>> adj = new ArrayList<ArrayList<int[]>>();
    for (int i = 0; i < n; ++i) adj.add(new ArrayList<int[]>());
    for (int i = 0; i < m; ++i) {
      int src = sc.nextInt();
      int dst = sc.nextInt();
      int edgeCost = sc.nextInt();
      adj.get(src).add(new int[] {dst, edgeCost});
    }

    // populate priority queue with neighbors of the source node 0
    for (int[] e : adj.get(source)) {
      pq.add(new int[] {e[0], e[1]});
    }

    while (!pq.isEmpty() && cost.size() < n) {
      int[] v = pq.remove(); // cheapest vertex
      if (!cost.containsKey(v[0])) {
        cost.put(v[0], v[1]);
        for (int[] e : adj.get(v[0])) {
          pq.add(new int[] {e[0], v[1] + e[1]});
        }
      }
    }

    for (int i = 0; i < n; ++i) {
      if (cost.containsKey(i)) {
        System.out.println(cost.get(i));
      } else {
        System.out.println("INF");
      }
    }
  }
}