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.*;

public class Main {

	private class Edge implements Comparable<Edge> {

		int from;
		int to;
		int cost;

		public Edge(int a, int b, int c) {
			from = a;
			to = b;
			cost = c;
		}

		@Override
		public int compareTo(Edge other) {

			return cost - other.cost;
		}

	}

	@SuppressWarnings("unchecked")
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		Main obj = new Main();

		int vertex = sc.nextInt();
		int edge = sc.nextInt();

		int source = sc.nextInt();

		int[] cost = new int[vertex];

		ArrayList<Edge>[] graph = new ArrayList[vertex];
		for (int i = 0; i < vertex; i++) {
			cost[i] = 1 << 30;
			graph[i] = new ArrayList<Edge>();
		}

		for (int i = 0; i < edge; i++) {
			int a = sc.nextInt();
			int b = sc.nextInt();
			int c = sc.nextInt();

			graph[a].add(obj.new Edge(a, b, c));
		}

		HashSet<Integer> visited = new HashSet<>();
		PriorityQueue<Edge> pq = new PriorityQueue<>();

		cost[source] = 0;
		pq.add(obj.new Edge(source, source, 0));

		while (!pq.isEmpty()) {
			Edge e = pq.poll();
			if (visited.contains(e.to)) {
				continue;
			}
			visited.add(e.to);
			cost[e.to] = e.cost;

			for (Edge f : graph[e.to]) {
				pq.offer(obj.new Edge(f.from, f.to, f.cost + e.cost));
			}

		}
		for (int e : cost) {
			if (e != 1 << 30) {
				System.out.println(e);
			} else {
				System.out.println("INF");
			}
		}

	}

}