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.*;

class Main{
        public static void main(String[] args) throws Exception{
            Scanner s = new Scanner(System.in);
            int V = s.nextInt();
            int E = s.nextInt();
            int src = s.nextInt();

            HashMap<Integer, List<int[]>> graph = new HashMap<>(V);
            for(int i = 0; i < V; ++i){
                graph.put(i, new LinkedList<int[]>());
            }

            for(int i = 0; i < E; ++i){
                int x = s.nextInt();
                int y = s.nextInt();
                int weight = s.nextInt();

                graph.get(x).add(new int[] {y, weight});
            }

            int[] dist = new int[V];
            Arrays.fill(dist, Integer.MAX_VALUE);

            PriorityQueue<int[]> queue = new PriorityQueue<>(new Comparator<int[]>() {
                @Override
                public int compare(int[] o1, int[] o2) {
                    return o1[1] - o2[1];
                }
            });

            queue.offer(new int[]{src, 0});
            dist[src] = 0;

            while(!queue.isEmpty()){
                int[] vertex = queue.poll();

                for(int[] adj : graph.get(vertex[0])){
                    if(dist[adj[0]] > dist[vertex[0]] + adj[1]){
                        dist[adj[0]] = dist[vertex[0]] + adj[1];
                        queue.offer(adj);
                    }
                }
            }

            for(int i = 0; i < V; ++i){
                System.out.println(dist[i] == Integer.MAX_VALUE ? "INF" : dist[i]);
            }
        }
}