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 <iostream>
#define INF 1000000100
#define E 500010
#define V 100100

using namespace std;
int main(){
  int v, e, r, i, j, s[E], t[E], d[E], c[V];
  cin >> v >> e >> r;
  for (i = 0; i < e; ++i){
    cin >> s[i] >> t[i] >> d[i];
  }
  
  // initializing the cost array
  for (i = 0; i < V; ++i){
    c[i] = INF;
  }
  c[r] = 0;

  // the reason why v-1 is big enough for this loop:
  //  longest path would be length of v-1
  //  for each i, cost btw(i-1, i) gets shorter/equal
  for (i = 0; i < v; ++i){
    bool updated = false;
    for (j = 0; j < e; ++j){
      int start = s[j], goal = t[j], distance = d[j];
      if(c[start] < INF && c[start]+d[j]<c[goal]){
        c[goal] = c[start]+d[j];
        updated = true;
      }
    }
    if(!updated) break;
  }
  for (i = 0; i < v; ++i){
    if(c[i] == INF){
      cout << "INF" << endl;
    }else{
      cout << c[i] << endl;
    }
  }
}