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;

template<typename T>
struct E{
  int to;
  T cost;
};

template<typename T>
vector<T>dijkstra(vector<vector<E<T>>>g,int s){
  T inf=numeric_limits<T>::max();
  vector<T>d(g.size(),inf);
  using Type=pair<T,int>;
  using Container=vector<Type>;
  using Cmp=greater<Type>;
  priority_queue<Type,Container,Cmp>q; 
  d[s]=0;
  q.push({d[s],s});
  while(!q.empty()){
    T cost=q.top().first;
    int from=q.top().second;
    q.pop();
    if(d[from]!=cost)continue;
    for(auto e:g[from]){
      T next_cost=e.cost+cost;
      if(d[e.to]>next_cost){
        d[e.to]=next_cost;
        q.push({d[e.to],e.to});
      }
    }
  }
  return d;
}

int main(){
  int N,M,S;
  cin>>N>>M>>S;
  vector<vector<E<int>>>G(N);
  for(int i=0;i<M;i++){
    int a,b,c;
    cin>>a>>b>>c;
    G[a].push_back({b,c});
  }
  auto ans=dijkstra<int>(G,S);
  for(auto it:ans){
    if(it==INT_MAX)cout<<"INF"<<endl;
    else cout<<it<<endl;
  }
  return 0;
}