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.IOException;
import java.io.InputStream;
import java.util.HashSet;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;
import java.util.Set;
 
public class Main {
	private static FastScanner sc = new FastScanner();
	static Node[] V;
	
	public static void main(String[] args) {
		int Vn = sc.nextInt();
		int En = sc.nextInt();
		int r = sc.nextInt();
		
		V = new Node[Vn]; 
		for(int i=0; i<Vn; i++) {
			V[i] = new Node();
		}
		
		for(int i=0; i<En; i++) {
			int s = sc.nextInt();
			int t = sc.nextInt();
			int d = sc.nextInt();
			V[s].nbr.add(new Edge(t, d));
		}
		
		PriorityQueue<Node> cdt = new PriorityQueue<>((a, b) -> a.min - b.min);
		cdt.add(V[r]);
		V[r].min = 0;
		
		while(!cdt.isEmpty()) {
			Node n = cdt.poll();
			for(Edge e : n.nbr) {
				if(n.min + e.d < V[e.t].min) {
					V[e.t].min = n.min + e.d;
					if(cdt.contains(V[e.t])) {
						cdt.remove(V[e.t]);
					}
					cdt.add(V[e.t]);
				}
			}
		}
		
		StringBuilder ans = new StringBuilder();
		for(int i=0; i<Vn; i++) {
			if(V[i].min == Integer.MAX_VALUE) {
				ans.append("INF");
			} else {
				ans.append(V[i].min);
			}
			ans.append("\n");
		}
		System.out.print(ans);
	}
	
	static class Node {
		int min = Integer.MAX_VALUE;
		Set<Edge> nbr = new HashSet<>();
	}
	
	static class Edge {
		int t;
		int d;
		
		Edge(int t, int d) {
			this.t = t;
			this.d = d;
		}
	}
	
	static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if(ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch(IOException e) {
                    e.printStackTrace();
                }
                if(buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
        public boolean hasNext() { skipUnprintable(); return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public int nextInt(){
            return Integer.parseInt(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
    }
}