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>
#define rep(i, n) for (int i=0; i<(n); i++)
#define P pair<int, int>
#define ll long long
using namespace std;

struct edge {int to, cost; };

const int MAX_V=100000;
const int INF=1000000001;

int V,E;
vector<edge> G[MAX_V+1];
int d[MAX_V+1];

void dijkstra(int s) {
  priority_queue<P, vector<P>, greater<P>> que;
  fill(d, d+V, 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 (int i=0; i<G[v].size(); i++) {
      edge e=G[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));
      }
    }
  }
}

int main() {
  cin>>V>>E;
  int s; cin>>s;
  rep(i, E) {
    int a,b,c; cin>>a>>b>>c;
    G[a].push_back(edge{b, c});
  }
  dijkstra(s);
  rep(i, V) {
    if (d[i]==INF) cout<<"INF"<<endl;
    else cout<<d[i]<<endl;
  }
}