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.*;

// djkstra ??????????????????
public class Main {

    static final int INF = Integer.MAX_VALUE;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int vn = sc.nextInt();
        int ve = sc.nextInt();
        int s = sc.nextInt();

        // List<Edge>[] edges = new ArrayList<Edge>[vn];
        List<List<Edge>> edges = new ArrayList<>();

        for (int i = 0; i < vn; i++) {
            edges.add(new ArrayList<>());
        }

        for (int i = 0; i < ve; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            int f = sc.nextInt();
            edges.get(a).add(new Edge(a, b, f));
            // ????????°??????
            // edges[b].add(new Edge(b, a, f));
        }

        int[] distance = new int[vn];
        Arrays.fill(distance, INF);
        distance[s] = 0;
        Queue<Edge> queue = new PriorityQueue<>();
        queue.add(new Edge(s, s, 0));

        while (!queue.isEmpty()) {
            Edge e1 = queue.poll();
            if (distance[e1.target] < e1.cost) {
                continue;
            }

            for (Edge e2 : edges.get(e1.target)) {
                if (distance[e2.target] > distance[e1.target] + e2.cost) {
                    distance[e2.target] = distance[e1.target] + e2.cost;
                    queue.add(new Edge(e1.target, e2.target, distance[e2.target]));
                }
            }
        }

        for (int i = 0; i < vn; i++) {
            System.out.println(distance[i] == INF ? "INF" : distance[i]);
        }
    }

    static class Edge implements Comparable<Edge> {
        public int source;
        public int target;
        public int cost;

        public Edge(int source, int target, int cost) {
            this.source = source;
            this.target = target;
            this.cost = cost;
        }


        @Override
        public int compareTo(Edge o) {
            return this.cost - o.cost;
        }
    }
}