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:
#if 0
time: 50min
using priority_queue(reverse) to save time.		
#endif
#include <iostream>
#include <queue>
#include <algorithm>
#include <utility>

using namespace std;

const int Inf = 10000*100000+100;
int a,b,V,E,R,S,Start[500000+10],To[500000+10],Dis[500000+10],N[500000+10];
int Ans[100000+10];

priority_queue<pair<int,int>,vector<pair<int,int> >,greater<pair<int,int> > > Q;


int main() {
	cin >> V >> E >> R;
	for (int i=1; i<=E; i++){
		cin >> S >> To[i] >> Dis[i];
		N[i] = Start[S];
		Start[S] = i;
	}
	
	fill(Ans,Ans+100010,Inf);
	Ans[R] = 0;
	Q.push(make_pair(0,R));
	
	while(!Q.empty()){
		a = Q.top().first;
		b = Q.top().second;
		Q.pop();
		if (Ans[b] == a){
			for(int i=Start[b]; i; i=N[i]){
				int t = To[i];
				if (a+Dis[i] < Ans[t]){
					Ans[t] = a+Dis[i];
					Q.push(make_pair(Ans[t],t));
				}
			}
		}	
	}
	
	for (int i=0; i<V; i++){
		if (Ans[i] < Inf){
			cout << Ans[i] << endl;
		}else{
			cout << "INF" << endl;
		}
	}	
}