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>
#include <queue>
#include <algorithm>
#define INF 1000000000
using namespace std;


struct edge{int to, cost;};
vector<edge> A[100000];
int d[100000];
typedef pair<int,int> P;

int main(){
  int V,E,R;
  cin >> V >> E >> R;
  for(int i=0;i<E;i++){
    int s,t,d;
    cin >> s >> t >> d;
    edge a;
    a.to=t;
    a.cost=d;
    A[s].push_back(a);
  }
  priority_queue<P, vector<P>, greater<P>> que;
  fill(d,d+V,INF);
  d[R]=0;
  que.push(P(0,R));
  while(!que.empty()){
    P p=que.top();que.pop();
    int v=p.second;
    if(d[v] < p.first)continue;
    for(int i=0;i < A[v].size();i++){
      edge e = A[v][i];
      if(d[e.to] > d[v]+e.cost){
        d[e.to]=d[v]+e.cost;
        que.push(P(d[e.to],e.to));
      }
    }
  }
  for(int i=0;i<V;i++){
    if(d[i]==INF){
      cout << "INF" << endl;
    }else{
      cout << d[i] << endl;
    }
  }
}