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.Arrays;
  
class Main{
  
static final int INF=Integer.MAX_VALUE/2;
static final PrintWriter out=new PrintWriter(System.out);
  
  
static class Edge{
int from;
int to;
int cost;
Edge(int from,int to,int cost){
this.from=from; this.to=to; this.cost=cost;
}
}
  
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()){
int v=Integer.parseInt(line.split(" ")[0]);
int e=Integer.parseInt(line.split(" ")[1]);
int r=Integer.parseInt(line.split(" ")[2]);
Edge[] es=new Edge[e];
int[] d=new int[v];
for(int i=0;i<e;i++){
line=br.readLine();
int s=Integer.parseInt(line.split(" ")[0]);
int t=Integer.parseInt(line.split(" ")[1]);
int c=Integer.parseInt(line.split(" ")[2]);
es[i]=new Edge(s,t,c);
}
BellmanFord(e,r,es,d);
for(int i=0;i<v;i++){
if(d[i]==INF){
out.println("INF");
}
else{
out.println(d[i]);
}
}
out.flush();
}
}
  
private static void BellmanFord(int ee,int r,Edge[] es,int[] d){
Arrays.fill(d,INF);
d[r]=0;
while(true){
boolean update=false;
for(int i=0;i<ee;i++){
Edge e=es[i];
if(d[e.to]>d[e.from]+e.cost){
d[e.to]=d[e.from]+e.cost;
update=true;
}
}
if(!update){
break;
}
}
}
}