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;
typedef pair<int64_t,int64_t> pii;

const int64_t INF = 1e16;
struct edge{ int64_t to, d; };

 
int main(){ 
  int64_t V, E, r;
  cin >> V >> E >> r;

  vector<vector<edge>> G(100010);
  for(int i=0; i<E; i++){
    int64_t s, t, d; cin >> s >> t >> d;
    G[s].push_back(edge{t,d});
  }

  priority_queue<pii, vector<pii>, greater<pii>> Q;
  vector<int64_t> dist(100010, INF);
  dist[r] = 0; Q.push(pii(0,r));

  while(!Q.empty()){
    int64_t cur_d = Q.top().first;
    int64_t cur_v = Q.top().second;
    Q.pop();

    if(cur_d > dist[cur_v]) continue;
  
    for(int i=0; i<G[cur_v].size(); i++){
      edge e = G[cur_v][i];
      if(dist[e.to] > dist[cur_v] + e.d){
        dist[e.to] = dist[cur_v] + e.d;
       Q.push(pii(cur_d + e.d, e.to));
      }
    }

  }

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