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;
using ll = long long;
using P = pair<ll, int>;

struct Edge { int to; ll cost; };
vector<Edge> G[100010];
ll INF = 1e18;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  int V, E; cin >> V >> E;
  vector<ll> d(V, INF);
  int v0; cin >> v0;

  for (int i = 0; i < E; i++) {
    int a, b; cin >> a >> b; // a--; b--;
    ll c; cin >> c;
    G[a].emplace_back(Edge({b, c}));
    // G[b].emplace_back(Edge({a, c}));
  }

  priority_queue<P, vector<P>, greater<P>> q;
  d[v0] = 0;
  q.push(P(0, v0));

  while (!q.empty()) {
    P p = q.top(); q.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;
        q.push(P(d[e.to], e.to));
      }
    }
  }

  for (int i = 0; i < V; i++) {
    if (d[i] == INF) cout << "INF\n";
    else cout << d[i] << '\n';
  }

  return 0;
}