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 {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int start = sc.nextInt();
		ArrayList<HashMap<Integer, Integer>> graph = new ArrayList<>();
		for (int i = 0; i < n; i++) {
		    graph.add(new HashMap<>());
		}
		for (int i = 0; i < m; i++) {
		    int a = sc.nextInt();
		    int b = sc.nextInt();
		    int c = sc.nextInt();
		    graph.get(a).put(b, c);
		}
		PriorityQueue<Path> queue = new PriorityQueue<>();
		queue.add(new Path(start, 0));
		int[] costs = new int[n];
		Arrays.fill(costs, Integer.MAX_VALUE);
		while (queue.size() > 0) {
		    Path p = queue.poll();
		    if (costs[p.idx] <= p.value) {
		        continue;
		    }
		    costs[p.idx] = p.value;
		    for (Map.Entry<Integer, Integer> entry : graph.get(p.idx).entrySet()) {
		        queue.add(new Path(entry.getKey(), p.value + entry.getValue()));
		    }
		}
		StringBuilder sb = new StringBuilder();
		for (int x : costs) {
		    if (x == Integer.MAX_VALUE) {
		        sb.append("INF");
		    } else {
		        sb.append(x);
		    }
		    sb.append("\n");
		}
		System.out.print(sb);
	}
	
	static class Path implements Comparable<Path> {
	    int idx;
	    int value;
	    
	    public Path(int idx, int value) {
	        this.idx = idx;
	        this.value = value;
	    }
	    
	    public int compareTo(Path another) {
	        return value - another.value;
	    }
	}
}