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.Arrays;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.stream.Stream;

public class Main{
	public static void main(String[] args){
		solve();
	}
	private static void solve() {
		// TODO ?????????????????????????????????????????????
		Scanner sc = new Scanner(System.in);
		int V = sc.nextInt();
		int E = sc.nextInt();
		int r = sc.nextInt();
		@SuppressWarnings("unchecked")
		List<Edge>[] edges = Stream.generate(ArrayList::new).limit(V).toArray(List[]::new);
		for(int i=0;i<E;i++){
			edges[sc.nextInt()].add(new Edge(sc.nextInt(), sc.nextInt()));
		}
		int[] dist = new int[V];
		int[] pred = new int[V];
		shortestPaths(edges, r, dist, pred);
		for(int i=0;i<V;i++){
			if(dist[i]==Integer.MAX_VALUE){
				System.out.println("INF");
				continue;
			}
			System.out.println(dist[i]);
		}
	}
	public static void shortestPaths(List<Edge>[] edges, int s, int[] prio, int[] pred) {
		Arrays.fill(pred, -1);
		Arrays.fill(prio, Integer.MAX_VALUE);
		prio[s] = 0;
		PriorityQueue<Long> q = new PriorityQueue<>();
		q.add((long) s);
		while (!q.isEmpty()) {
			long cur = q.remove();
			int curu = (int) cur;
			if (cur >>> 32 != prio[curu])
				continue;
			for (Edge e : edges[curu]) {
				int v = e.t;
				int nprio = prio[curu] + e.cost;
				if (prio[v] > nprio) {
					prio[v] = nprio;
					pred[v] = curu;
					q.add(((long) nprio << 32) + v);
				}
			}
		}
	}

	static class Edge {
		int t;
		int cost;

		public Edge(int t, int cost) {
			this.t = t;
			this.cost = cost;
		}
	}

}