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;
#define M 1000000007
#define f first
#define s second
typedef pair<int,int> P;
int n,m,r,i,j,a,b,c,x,y;
int sum[100000],flg[100000];
vector<int>  om[100000],hc[100000];
int main(void)
{
	P p;
	priority_queue<P,vector<P>,greater<P> > qu;
	
	cin>>n>>m>>r;
	for(i=0;i<n;i++) sum[i]=M,flg[i]=0;
	for(i=0;i<m;i++){
		cin>>a>>b>>c;
		hc[a].push_back(b);
		om[a].push_back(c);
	}
	qu.push(P(0,r));
	sum[r]=0;
	while(qu.size()!=0){
		p=qu.top();
		qu.pop();
		if(flg[p.s]==0){
			flg[p.s]=1;
			for(i=0;i<om[p.s].size();i++){
				x=hc[p.s][i];
				y=om[p.s][i];
				if(sum[x]>p.f+y){
					sum[x]=p.f+y;
					qu.push(P(sum[x],x));
				}
			}
		}
	}
	for(i=0;i<n;i++) {
		if(sum[i]!=M) cout<<sum[i]<<endl;
		else cout<<"INF"<<endl;
	}
	return 0;
}