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 long long ll;

const ll inf = 0x3f3f3f3f3f3f3f3f;
const int mx = 100005;

ll dist[mx];
vector<pair<ll, int> > adj[mx];
bitset<mx> inq;
int v, e, r;
int q[mx], qh, qt;

int qpop() {
  int v = q[qh++];
  if (qh > mx) qh = 0;
  return v;
}

void qpush(int v) {
  q[qt++] = v;
  if (qt > mx) qt = 0;
}

int main() {
  qh = qt = 0;
  cin >> v >> e >> r;
  for (int i = 0; i < v; i++)
    dist[i] = inf;
  for (int i = 0; i < e; i++) {
    int s, t, d; cin >> s >> t >> d;
    adj[s].push_back({ d, t });
  }
  dist[r] = 0;
  qpush(r);
  while (qh != qt) {
    int p = qpop();
    inq[p] = false;
    for (auto h : adj[p]) {
      int t = h.second;
      ll d = h.first + dist[p];
      if (d < dist[t]) {
	dist[t] = d;
	if (!inq[t])
	  inq[t] = true, qpush(t);
      }
    }
  }
  for (int i = 0; i < v; i++) {
    if (dist[i] < inf / 2) cout << dist[i] << endl;
    else cout << "INF" << endl;
  }
}