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 lint;

#define MAX_N 100010
//d,edge,g,P,q
lint d[MAX_N];
struct edge{
	int to;
	lint cost;
};
vector<edge> g[MAX_N];
typedef pair<lint,int> P;
priority_queue<P,vector<P>,greater<P> > q;

void pfs(int s){
	d[s]=0;q.push({0,s});
	lint cd;int v;
	while(q.size()){
		cd=q.top().first;v=q.top().second;q.pop();
		if(d[v]<cd)continue;
		for(edge &e:g[v])if(cd+e.cost<d[e.to]){
			d[e.to]=cd+e.cost;
			q.push({d[e.to],e.to});
		}
	}
}

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);cout.tie(0);

	lint v,e,r;cin>>v>>e>>r;
	for(int i=0;i<v;++i)d[i]=INT_MAX;
	int a,b;lint c;
	for(int i=0;i<e;++i){
		cin>>a>>b>>c;
		g[a].push_back({b,c});
	}pfs(r);
	for(int i=0;i<v;++i){
		if(d[i]==INT_MAX)cout<<"INF\n";
		else cout<<d[i]<<endl;
	}
}