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.*;
import java.io.*;

public class Main {

	static int vertex;
	static int edges;
	static boolean[] visited;
	static int[] cost;
	static int[] parent;
	static ArrayList<Edge>[] graph;
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static final int INFINITY = Integer.MAX_VALUE;
	static Main obj = new Main();
	static int start;

	class Edge implements Comparable<Edge> {

		int from;
		int to;
		int weight;

		public Edge(int from, int to, int weight) {
			this.from = from;
			this.to = to;
			this.weight = weight;
		}

		@Override
		public int compareTo(Edge other) {
			int diff = weight - other.weight;
			return diff;
		}

	}

	public static void main(String[] args) throws IOException {

		input();
		prim(start);

	}

	@SuppressWarnings("unchecked")
	public static void input() throws IOException {
		StringTokenizer st = new StringTokenizer(br.readLine());
		vertex = Integer.parseInt(st.nextToken());
		edges = Integer.parseInt(st.nextToken());
		start = Integer.parseInt(st.nextToken());
		visited = new boolean[vertex];
		cost = new int[vertex];
		parent = new int[vertex];
		graph = new ArrayList[vertex];
		for (int i = 0; i < graph.length; i++) {
			graph[i] = new ArrayList<Edge>();
		}
		for (int i = 0; i < edges; i++) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (Exception e) {
				break;
			}
			int a = Integer.parseInt(st.nextToken());
			int b = Integer.parseInt(st.nextToken());
			int c = Integer.parseInt(st.nextToken());

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

		}
		for (int i = 0; i < cost.length; i++) {
			cost[i] = INFINITY;
		}

	}

	public static void prim(int a) {

		int added = 1;
		visited[a] = true;
		cost[a] = 0;
		PriorityQueue<Edge> pq = new PriorityQueue<Edge>();
		for (Edge e : graph[a]) {
			pq.offer(e);
			cost[e.to] = e.weight;
		}
		while (!pq.isEmpty()) {
			Edge e = pq.poll();
			if (visited[e.to]) {
				continue;
			}
			for (Edge f : graph[e.to]) {
				if (cost[f.to] > f.weight + e.weight) {
					cost[f.to] = f.weight + e.weight;
					parent[f.to] = e.to;
					pq.offer(obj.new Edge(e.to,f.to,cost[f.to]));
				}
			}
			visited[e.to] = true;
			added++;
			if (added == vertex) {
				break;
			}

		}
		for (int i = 0; i < vertex; i++) {
			if (cost[i] == Integer.MAX_VALUE) {
				System.out.println("INF");
			} else {
				System.out.println(cost[i]);
			}
		}

	}

}
/*
 * Edge e = pq.poll(); // if (visited[e.to]) { // continue; // }
 * 
 * if (cost[e.to] >= e.weight + cost[e.from]) { cost[e.to] = e.weight +
 * cost[e.from]; parent[e.to] = e.from; visited[e.to] = true; sum += e.weight;
 * added++; } else { continue; } if (added == vertex) { break; } for (Edge q :
 * graph[e.to]) { if (visited[q.to]) { continue; } else { pq.offer(q); } }
 */