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.*;
import java.util.StringTokenizer;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.PriorityQueue;
import java.util.Comparator;
    
class Main{
    
static final int INF=Integer.MAX_VALUE/2;
static final PrintWriter out=new PrintWriter(System.out);
    
static class Pair{
int x;
int y;
Pair(int x,int y){
this.x=x; this.y=y;
}
static final Comparator<Pair> DISTANCE_ORDER=new DistanceOrderComparator();
public static class DistanceOrderComparator implements Comparator<Pair>{
public int compare(Pair p1,Pair p2){
return (p1.x>p2.x)?1:(p1.x<p2.x)?-1:0;
}
}
}

static class Edge{
int to;
int cost;
Edge(int to,int cost){
this.to=to; this.cost=cost;
}
}

static class MyArrayList extends ArrayList<Edge>{}
    
public static void main(String[] args) throws IOException{
BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
String line="";
while((line=br.readLine())!=null&&!line.isEmpty()){
StringTokenizer st1=new StringTokenizer(line);
int v=Integer.parseInt(st1.nextToken());
int e=Integer.parseInt(st1.nextToken());
int r=Integer.parseInt(st1.nextToken());
MyArrayList[] array=new MyArrayList[v];
int[] d=new int[v];
for(int i=0;i<v;i++) array[i]=new MyArrayList();
for(int i=0;i<e;i++){
line=br.readLine();
StringTokenizer st2=new StringTokenizer(line);
int s=Integer.parseInt(st2.nextToken());
int t=Integer.parseInt(st2.nextToken());
int c=Integer.parseInt(st2.nextToken());
array[s].add(new Edge(t,c));
}
djkstra(r,d,array);
for(int i=0;i<v;i++){
out.println((d[i]==INF)?"INF":d[i]);
}
out.flush();
}
}

private static void djkstra(int r,int[] d,MyArrayList[] array){
PriorityQueue<Pair> pque=new PriorityQueue<Pair>(1,Pair.DISTANCE_ORDER);
Arrays.fill(d,INF);
d[r]=0;
pque.offer(new Pair(0,r));
while(!pque.isEmpty()){
Pair p=pque.poll();
int v=p.y;
ArrayList<Edge> list=array[v];
if(d[v]<p.x||list.size()==0) continue;
for(int i=0;i<list.size();i++){
Edge e=list.get(i);
int to=e.to;
int dv=d[v];
int cost=e.cost;
if(d[to]>dv+cost){
d[to]=dv+cost;
pque.offer(new Pair(d[to],to));
}
}
}
}
}