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 <vector>
#include <queue>
#include <utility>
using namespace std;

int V,E,r;
const int Inf = 10000*100000+100;
int C[100010];
int main(){
	while(cin >> V >> E >> r && V >0){
		vector< vector< pair<int,int> > > v(V+10);
		for(int i=0;i<E;i++){
			int s,t,d;
			cin >> s >> t >> d;
			v[s].push_back(make_pair(d,t));
		}
		priority_queue<pair <int,int> > P;
		P.push(make_pair(0,r));
		for(int i=0;i<V;i++){
			C[i] = Inf;
		}
		C[r] = 0;
		while(!P.empty()){
			pair<int,int> t = P.top();
			int s = t.second;
			P.pop();
			if(C[s] < t.first) continue;
			for(int i=0;i<v[s].size();i++){
				pair<int,int> e = v[s][i];
				if(C[e.second] > C[s] + e.first){
					C[e.second] = C[s] + e.first;
					P.push(make_pair(-C[e.second],e.second));
				}
			}
		}
		for(int i=0;i<V;i++){
			if(C[i] < Inf) cout << C[i] << endl;
			else cout << "INF" << endl;
		}
	}
}