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<bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<ll, int> pll;

vector<pll> graph[100100];
ll dist[100100];
int v,e;

#define INF (1ll << 60)

void dijkstra(int s){
	int from,i,to;
	ll d,l;
	pll tmp;
	priority_queue<pll, vector<pll>, greater<pll> > pq;
	fill(dist,dist+v,INF);
	dist[s]=0;
	pq.push(pll(dist[s],s));
	while(!pq.empty()){
		tmp = pq.top();
		pq.pop();
		from = tmp.second;
		d = tmp.first;
		for(i=(graph[from].size()-1); i>=0; i--){
			to = graph[from][i].second;
			l = graph[from][i].first;
			if(dist[to] > d+l){
				dist[to] = d+l;
				pq.push(pll(dist[to],to));
			}
		}
	}
}

int main(void){
	int i,s,t,r;
	ll d;
	cin >> v >> e >> r;
	for(i=0; i<e; i++){
		cin >> s >> t >> d;
		graph[s].push_back(pll(d,t));
	}
	dijkstra(r);
	for(i=0; i<v; i++){
		if(dist[i] == INF){
			cout << "INF" << endl;
		}else{
			cout << dist[i] << endl;
		}
	}
	return 0;
}