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 <utility>
using namespace std;
const int INF = (1e9);

vector<int> dijkstra(vector< vector< pair<int,int> > > &G, int s){
  vector<int> ret(G.size(),INF);
  priority_queue< pair<int,int> > wait;
  wait.emplace(0,s);
  while(!wait.empty()){
    int c = -wait.top().first, v = wait.top().second;
    wait.pop();
    if(ret[v] < c) continue;
    ret[v] = c;
    for(size_t i = 0; i < G[v].size(); ++i){
      int c_ = c + G[v][i].first, v_ = G[v][i].second;
      if(c_ < ret[v_]){
        ret[v_] = c_;
        wait.emplace(-c_,v_);
      }
    }
  }
  return ret;
}

int main(){
  int V, E, r;
  cin >> V >> E >> r;
  vector< vector< pair<int,int> > > G(V);
  for(int i = 0; i < E; ++i){
    int s, t, d;
    cin >> s >> t >> d;
    G[s].emplace_back(d,t);
  }
  vector<int> ans = dijkstra(G,r);
  for(int i = 0; i < V; ++i){
    if(ans[i] < INF) cout << ans[i] << endl;
    else cout << "INF" << endl;
  }
  return 0;
}