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 ll;
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
#define MOD 1000000007
#define INF 1000000000000000
#define fi first
#define se second
#define all(v) v.begin(),v.end()
int dx[]={0,1,0,-1},dy[]={1,0,-1,0};
#define pb push_back
struct edge{int to,cost;};
typedef pair<int,int> P;
int n,m,r,d[111111];
vector<edge>v[111111];
void dijkstra(int x){
	fill(d,d+n,INF);
	d[x]=0;
	priority_queue<P,vector<P>,greater<P>>q;
	q.push({x,0});
	while(!q.empty()){
		P p=q.top();
		q.pop();
		for(edge e:v[p.first]){
			if(d[e.to]>d[p.first]+e.cost){
				d[e.to]=d[p.first]+e.cost;
				q.push({e.to,d[e.to]});
			}
		}
	}
}
signed main(){
	cin>>n>>m>>r;
	rep(i,m){
		int a,b,c;
		cin>>a>>b>>c;
		v[a].pb({b,c});
	}
	dijkstra(r);
	rep(i,n){
		if(d[i]==INF)puts("INF");
		else cout<<d[i]<<endl;
	}
	return 0;
}