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>
#include<queue>
using namespace std;
#define MAX_VAL 100000
#define INF 4123456789123456

typedef long long ll;
typedef pair<ll,ll> P;

struct edge{ll to, cost;};

vector<edge> G[MAX_VAL];
ll d[MAX_VAL], V;

void dijkstra(ll s){
	priority_queue<P,vector<P>,greater<P>> q;
	fill(d,d+V, INF);
	
	d[s] = 0;
	q.push(P(0,s));
	
	while(!q.empty()){
		P p = q.top();q.pop();
		ll v = p.second;
		
		if(d[v] < p.first) continue;
		
		for(edge e : G[v]){
			if(d[e.to] > d[v] + e.cost){
				d[e.to] = d[v] + e.cost;
				q.push(P(d[e.to],e.to));
			}
		}
	}
	
	
}

int main(){
	struct edge e;
	ll E, r, s;
	
	cin>>V>>E>>r;
	
	for(int i = 1; i <= E; i++){
		cin>>s>>e.to>>e.cost;
		G[s].push_back(e);
	}
	
	dijkstra(r);
	
	for(int i = 0; i < V; i++)
		cout<<(d[i]==INF?"INF":to_string(d[i]))<<endl;
	
	return 0;
}