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 <queue>
#include <algorithm>
#include <vector>
#include <climits>
#define int long long
using namespace std;
typedef pair <int,int> P;
#define to first
#define co second
#define fi first
#define se second
const int INF=INT_MAX;
const int MAX_N=100000;
vector <P> G[MAX_N];
int n,d[MAX_N];
void dijk(int s){
  priority_queue <P,vector<P>,greater<P> > que;
  fill(d,d+n,INF);
  d[s]=0;
  que.push(P(0,s));
  for(;!que.empty();){
    P p=que.top(); que.pop();
    int v=p.se;
    if (d[v]<p.fi) continue;
    for(int i=0;i<G[v].size();i++){
      P e=G[v][i];
      if(d[e.to]>d[v]+e.co){
	d[e.to]=d[v]+e.co;
	que.push(P(d[e.to],e.to));
      }
    }
  }
}
signed main(){
  int e,r;
  cin>>n>>e>>r;
  for(int i=0,a,b,c;i<e;i++){
    cin>>a>>b>>c;
    G[a].push_back(make_pair(b,c));
  }
  dijk(r);
  for(int i=0;i<n;i++){
    if(d[i]==INF) cout<<"INF"<<endl;
    else cout<<d[i]<<endl;
  }
  return 0;
}