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;

int main() {
  ll V, E, r;  cin >> V >> E >> r;
  vector<vector<pair<ll, ll>>> map(V);
  rep(i, E) {
    ll s, t, d; cin >> s >> t >> d;
    map[s].push_back(make_pair(t, d));
//    map[t].push_back(make_pair(s, d));
  }
  
  ll dis[V]; memset(dis, -1, sizeof(dis));
  priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>> pq;
  pq.push(make_pair(0, r));
  dis[r] = 0;
  vector<bool> checked(V, false);
  while(!pq.empty()) {
    auto p = pq.top(); pq.pop();
    ll a = p.second, b = p.first;
    if (checked[a] == true) continue;
    checked[a] = true;
    dis[a] = b;
    
    for (auto v : map[a]) {
      pq.push(make_pair((b + v.second), v.first));
//      dis[v.first] = b + v.second;
    }
  }
  
  rep(i, V) {
    if (dis[i] == -1)  cout << "INF" << endl;
    else  cout << dis[i] << endl;
  }
}