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 int ll;
typedef pair<ll,ll> mp;
#define inf 1e9

vector<ll> daikus(vector<vector<mp> > &g,int s){
	ll v = g.size();
	vector<ll> res(v,inf);
	priority_queue<mp,vector<mp>,greater<mp> > q;
	q.push(mp(0,s) );
	while(!q.empty()){
		mp now = q.top();
		q.pop();
		ll nn = now.second;
		ll cost = now.first;
		if( res[nn] < cost) continue;
		res[nn] = cost;
		for(int i=0;i<g[nn].size();i++){
			ll next = g[nn][i].second;
			ll nc = cost + g[nn][i].first;
			if( res[next] < cost ) continue;
			q.push( mp(nc,next) );
		}
	}
	return res;
}

int main(){
	
    ll v,e,r;
    cin>>v>>e>>r;
    vector<vector<mp> > g(v);
    for(int i=0;i<e;i++){
	ll s,t,d;
	cin>>s>>t>>d;
	g[s].push_back( mp(d,t) );
	//g[t].push_back( mp(d,s) );
    }
    vector<ll> res = daikus(g,r);
    for(int i=0;i<v;i++)if(res[i] == inf) cout<<"INF"<<endl;
    else cout<<res[i]<<endl;
	return 0;
}