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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.PriorityQueue;

public class Main {

    static class edge{
        int from, to, cost;
    }

    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] str = br.readLine().split(" ");
        int v = Integer.parseInt(str[0]);
        int e = Integer.parseInt(str[1]);
        int r = Integer.parseInt(str[2]);

        @SuppressWarnings("unchecked")
        ArrayList<edge>[] es = new ArrayList[v];
        for(int i=0; i<v; i++) es[i] = (new ArrayList<>());

        for (int i=0; i<e; i++){
            str = br.readLine().split(" ");
            edge ed = new edge();
            ed.from = Integer.parseInt(str[0]);
            ed.to = Integer.parseInt(str[1]);
            ed.cost = Integer.parseInt(str[2]);
            es[ed.from].add(ed);
        }

        PriorityQueue<long[]> dist = new PriorityQueue<>((long[] le, long[] ri) -> (int)(le[0] - ri[0]));
        long[] vertex = new long[2];
        vertex[0] = 0;
        vertex[1] = r;
        dist.add(vertex);

        long[] len = new long[v];
        Arrays.fill(len, Long.MAX_VALUE);
        len[r] = 0;

        while(!dist.isEmpty()){
            vertex = dist.poll();

            long u = vertex[1];
            for (Object ed: es[(int)u]){
                if(len[((edge) ed).from] + ((edge) ed).cost < len[((edge) ed).to]) {
                    len[((edge) ed).to] = len[((edge) ed).from] + ((edge) ed).cost;
                    long[] p = new long[2];
                    p[0] = len[((edge) ed).to];
                    p[1] = ((edge) ed).to;
                    dist.add(p);
                }
            }
        }

        for(int i=0; i<v; i++){
            if(len[i] == Long.MAX_VALUE){
                System.out.println("INF");
            } else {
                System.out.println(len[i]);
            }
        }
    }
}