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;
#define rep(i,n) for(int i = 0; i < (int)n; i++)
using ll = long long;
struct edge{int to; ll cost;};
using P = pair<ll,int>;
const ll INF = 1e17;

void dijkstra(int n, int s, vector<vector<edge>>& g, vector<ll>& d){
  priority_queue<P,vector<P>,greater<P>> que;
  rep(i,n) d[i] = INF;
  d[s] = 0;
  que.push(P(0,s));
  while(!que.empty()){
    P p = que.top();
    que.pop();
    int v = p.second;
    if(d[v] < p.first) continue;
    for(auto e : g[v]){
      if(d[e.to] > d[v] + e.cost){
        d[e.to] = d[v] + e.cost;
        que.push(P(d[e.to], e.to));
      }
    }
  }
}

int main(){
  int v, e, r;
  cin >> v >> e >> r;
  vector<vector<edge>> g(v);
  rep(i,e) {
    int s, t; ll d;
    cin >> s >> t >> d;
    g[s].push_back(edge{t,d});
  }
  vector<ll> d(v,INF);
  dijkstra(v,r,g,d);
  rep(i,v) cout << (d[i] == INF ? "INF" : to_string(d[i]))  << endl;
  return 0;
}