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 CPP):

Solution:
#include<bits/stdc++.h>
#define MAX INT_MAX
#define F first
#define S second
using namespace std;
typedef pair<int,int> P;
vector<int> town[100000],cost[100000];
int main(void)
{
	int V,E,R;
	int S,T,D;
	int flg[100000];
	int length[100000];
	
	int X,Y;
	int i;
	priority_queue<P,vector<P>,greater<P>> que;
	P pp;
	
	cin>>V>>E>>R;
	
	for(i=0;i<E;i++){
		cin>>S>>T>>D;
		town[S].push_back(T);
		cost[S].push_back(D);
	}
	
	fill(length,length+V,MAX);
	fill(flg,flg+V,0);
	
	que.push(P(0,R));
	while(que.size()!=0){
		pp=que.top();
		que.pop();
		X=pp.F;
		Y=pp.S;
		if(X<length[Y]){
			length[Y]=X;
			flg[Y]=1;
			
			for(i=0;i<town[Y].size();i++){
				if(flg[town[Y][i]]==0){
					que.push(P(X+cost[Y][i],town[Y][i]));
				}
			}
		}
	}
	
	for(i=0;i<V;i++){
		if(length[i]==MAX){
			cout<<"INF"<<endl;
		}
		else{
			cout<<length[i]<<endl;
		}
	}
	return 0;
}