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 <queue>
#include <algorithm>
#include <utility>

using namespace std;

const int Inf = 10000*100000+100;
int V,E,R,S,T[500000+10],D[500000+10],H[500000+10],N[500000+10];
int C[100000+10],P[100000+10];

int main() {
	queue<int> Q;
	cin >> V >> E >> R;
	for (int i=1; i<=E; i++){
		cin >> S >> T[i] >> D[i];
		N[i] = H[S];
		H[S] = i;
	}
	fill(C,C+100010,Inf);
	C[R] = 0;
	Q.push(R);
	P[R] = 1;
	while(!Q.empty()){
		int u = Q.front();
		Q.pop();
		P[u] = 0;
		for (int i=H[u]; i; i=N[i]){
			int t = T[i];
			if (C[t] > C[u] + D[i]){
				C[t] = C[u]+D[i];
				if (!P[t]){
					Q.push(t);
					P[t] = 1;
				}	
			}
		}
	}
	
	for (int i=0; i<V; i++){
		if (C[i] < Inf){
			cout << C[i] << endl;
		}else{
			cout << "INF" << endl;
		}
	}	
}