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;

public class Main {

	public static void main(String[] args) {

		new Main().run();
	}

	@SuppressWarnings("unchecked")
	private void run() {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int m = scanner.nextInt();
		int s = scanner.nextInt();
		List<Pair>[] lists = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			lists[i] = new ArrayList<Pair>();
		}
		for (int i = 0; i < m; i++) {
			int v = scanner.nextInt();
			int a = scanner.nextInt();
			int b = scanner.nextInt();
			lists[v].add(new Pair(a, b));
		}
		PriorityQueue<Pair> pq = new PriorityQueue<Pair>();
		pq.add(new Pair(s, 0));
		int[] cost = new int[n];
		Arrays.fill(cost, Integer.MAX_VALUE);
		cost[s] = 0;
		while (!pq.isEmpty()) {
			Pair pair = pq.poll();
			if (cost[pair.a] < pair.b)
				continue;
			for (Pair p : lists[pair.a]) {
				if (cost[p.a] > pair.b + p.b) {
					cost[p.a] = pair.b + p.b;
					pq.offer(new Pair(p.a, cost[p.a]));
				}
			}

		}
		for (int a : cost) {
			if (a == Integer.MAX_VALUE )
				System.out.println("INF");
			else
				System.out.println(a);
		}

	}

	class Pair implements Comparable<Pair> {
		int a, b;

		public Pair(int a, int b) {
			super();
			this.a = a;
			this.b = b;
		}

		@Override
		public String toString() {
			return "Pair [a=" + a + ", b=" + b + "]";
		}

		@Override
		public int compareTo(Pair o) {
			return this.b - o.b;
		}

	}
}