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 <cstdio>
#include <vector>
#include <queue>
using namespace std;
const int MAX_V = 1e+5, INF = 1e+9;
struct edge {int to, cost;};
typedef pair<int, int> P;
int V, E, r, D[MAX_V]; vector<edge> G[MAX_V];

void dijkstra(int s) {
  fill(D, D+V, INF); D[r] = 0;
  priority_queue<P, vector<P>, greater<P>> q;
  q.push(P(0, s));
  while(!q.empty()) {
    P p = q.top(); q.pop();
    int now = p.second;
    if(D[now] < p.first) continue;
    for(int i = 0; i < G[now].size(); ++i) {
      edge e = G[now][i];
      if(D[e.to] > D[now] + e.cost) {
        D[e.to] = D[now] + e.cost;
        q.push(P(D[e.to], e.to));
      }
    }
  }
}
int main() {
  scanf("%d %d %d", &V, &E, &r);
  for(int i = 0, s, t, d; i < E; ++i) {
    scanf("%d %d %d", &s, &t, &d);
    edge e = {t, d};
    G[s].push_back(e);
  }
  dijkstra(r);
  for(int i = 0; i < V; ++i) {
    if(D[i] == INF) {
      printf("%s\n", "INF");
    } else {
      printf("%d\n", D[i]);
    }
  }
}