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<vector>
using namespace std;

int main(){
  int iv,ie,r;
  cin >> iv >> ie >> r;
  int d[100010];
  for (int i=0;i<iv;i++){
    d[i]= 1000000010;
  }
  d[r]=0;
  vector<pair<int,int> > w(ie);
  vector<int> cost(ie);
  for(int i=0;i<ie;i++){
    int s0,e0,d0;
    cin>>s0>>e0>>d0;
    w[i] = make_pair(s0,e0);
    cost[i]=d0;
  }
  for(int i=0;i<iv-1;i++){
    int k=0;
    for(int j=0;j<ie;j++){
      int s1,e1,d1;
      s1=w[j].first;
      e1=w[j].second;
      d1=cost[j];
      if(d[e1]>d[s1]+d1) k+=1;
      d[e1]=min(d[e1],d[s1]+d1);
    }
    if(k==0) break;
   }

  for(int i=0;i<iv;i++){
    if(d[i]==1000000010){
      cout<<"INF"<<endl;
    }else{
      cout<<d[i]<<endl;
    }
  }
}