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 <algorithm>
#include <map>
#include <vector>
using namespace std;
typedef long long ll;
#define INF 2147483647

struct edge{
	int to,cost;
};
int V,E; 

vector <edge> G[100010];

multimap <int,int> l;


ll d[500010];


void dijkstra(int s){
	fill(d,d+V,INF);
	d[s] = 0;
	
	l.insert(make_pair(0,s));
	
	while(l.size() > 0){
		int p = l.begin()->first;
		int v = l.begin()->second;
		l.erase(l.begin());
		
		if(d[v] < p) continue;
		
		for(int i = 0;i < G[v].size(); i++){
			edge e = G[v][i];
			if(d[e.to] > d[v] + e.cost){
				d[e.to] = d[v] + e.cost;
				l.insert(make_pair(d[e.to], e.to));
			}
		}
	}
}


int main(){
	
	int r;
	cin >> V >> E >> r;
	for(int i = 0;i < E; i++){
 		edge e;
		int from;
		cin >> from >> e.to >> e.cost;
		G[from].push_back(e);
	}
	
	dijkstra(r);
	
	for(int i = 0;i < V; i++){
		if(d[i] != INF) cout << d[i] << endl;
		else cout << "INF" <<endl;
	}
	return 0;
}