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.Arrays;
import java.util.Scanner;

class Main{
	public static void main(String args[]){
		try(Scanner sc=new Scanner(System.in)){
			int v=sc.nextInt();//頂点数
			int e=sc.nextInt();//辺数
			int r=sc.nextInt();//始点
			int inf=10000*100000+100;
			int[] c=new int[v+1];//始点からの距離
			int[] S=new int[e+1];
			int[] T=new int[e+1];
			int[] D=new int[e+1];
			Arrays.fill(c, inf);
			Arrays.fill(D, inf);
			for(int i=0; i<e; i++) {
				S[i]=sc.nextInt();
				T[i]=sc.nextInt();
				D[i]=sc.nextInt();
			}
			c[r]=0;
			for(int k=0; k<v; k++) {
				boolean update=false;
				for(int i=0; i<e; i++) {
					int s=S[i], t=T[i], d=D[i];
					if(c[s]<inf && c[s]+d<c[t]) {
						c[t]=c[s]+d;
						update=true;
					}
				}
				if(! update) break;
			}
			for(int i=0; i<v; i++) {
				if(c[i]==inf) {
					System.out.println("INF");
				}
				else {
					System.out.println(c[i]);
				}
			}
		}
	}
}