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 <iostream>
#include <algorithm>
#include <string>
#include <queue>
#include <vector>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
struct edge{int to, cost;};
#define INF 1000000001

int V,E;
vector<edge> G[100005];
int d[100005];

void dijkstra(int s){
	priority_queue<P, vector<P>,greater<P> > que;
	for(int i=0;i<V;i++)d[i]=INF;
	d[s]=0;
	que.push(P(0,s));
	
	while(!que.empty()){
		P p=que.top();que.pop();
		int v=p.second;
		if(d[v]<p.first)continue;
		for(int i=0;i<G[v].size();i++){
			edge e=G[v][i];
			if(d[e.to]>d[v]+e.cost){
				d[e.to]=d[v]+e.cost;
				que.push(P(d[e.to],e.to));
			}
		}
	}
}

int main(void){
	int r,s;edge e;
	cin>>V>>E>>r;
	for(int i=0;i<E;i++){
		cin>>s>>e.to>>e.cost;
		G[s].push_back(e);
	}
	dijkstra(r);
	for(int i=0;i<V;i++){
		if(d[i]==INF)cout<<"INF\n";
		else cout<<d[i]<<endl;
	}
	
	return 0;
}