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>
#define INF 50000000000000
std::vector<int> G[100000];
struct edge{int from,to,cost;};
int V,E,r;
edge es[500000];
long long int d[100000];
void shortest_path(int s);
int main(void){
	std::cin>>V>>E>>r;
	for(int i=0;i<E;i++){
		int from,to,cost;
		std::cin>>from>>to>>cost;
		//G[from].push_back(to);
		//G[t].push_back(s);
		es[i].from=from;
		es[i].to=to;
		es[i].cost=cost;
	}
	shortest_path(r);
	for(int i=0;i<V;i++){
		if(d[i]!=INF){
			std::cout<<d[i]<<std::endl;
		}else {
			std::cout<<"INF"<<std::endl;
		}
	}
	return 0;
}
void shortest_path(int s){
	for(int i=0;i<V;i++){
		d[i]=INF;
	}
	d[r]=0;
	while(1){
		bool flag=true;
		for(int i=0;i<E;i++){
			if(d[es[i].from]!=INF){
				if(d[es[i].to]>d[es[i].from]+es[i].cost){
					d[es[i].to]=d[es[i].from]+es[i].cost;
					flag=false;
				}
			}
		}
		if(flag){
			break;
		}
	}
}