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.List;
import java.util.PriorityQueue;
import java.util.Scanner;


public class Main {

	static class State { // →bの辺の重さw
		int b, w;
		public State(int b, int w) {
			this.b = b;
			this.w = w;
		}
	}
	static class PQ implements Comparable<PQ>{
		int now;
		int d;
		public PQ(int now, int d) {
			this.now = now;
			this.d = d;
		}
		public int compareTo(PQ p) {
			return this.d - p.d;
		}
	}
	
	public static void main(String[] args) throws Exception {
		try(Scanner sc = new Scanner(System.in)) {
			int V = sc.nextInt(); // 頂点数
			int E = sc.nextInt(); // 辺数
			int r = sc.nextInt(); // 初めの頂点
			int INF = Integer.MAX_VALUE;
			
			@SuppressWarnings("unchecked")
			List<State>[] edge = new ArrayList[V];
			for(int i=0; i<V; i++) {
				edge[i] = new ArrayList<State>();
			}
			PriorityQueue<PQ> pq = new PriorityQueue<>();
			for(int i=0; i<E; i++) {
				int s = sc.nextInt();
				int t = sc.nextInt();
				int d = sc.nextInt();
				edge[s].add(new State(t, d));
			}
			int[] dis = new int[V];
			boolean[] processed = new boolean[V];
			for(int i=0; i<V; i++) {
				dis[i] = INF;
				processed[i] = false;
			}
			
			dis[r] = 0;
			pq.add(new PQ(r, 0));
			while(! pq.isEmpty()) {
				PQ p = pq.poll();
				if(processed[p.now]) {
					continue;
				}
				processed[p.now] = true;
				for(State s : edge[p.now]) {
					if(p.d+s.w < dis[s.b]) {
						dis[s.b] = p.d + s.w;
						pq.add(new PQ(s.b, dis[s.b]));
					}
				}
			}
			for(long cost : dis) {
				if(cost >= INF)	System.out.println("INF");
				else	System.out.println(cost);
			}
		}
	}

}