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<stdio.h>
#include<queue>
#include<algorithm>
#include<vector>
using namespace std;
#define MAX_V 100001
#define INF (1e9 + 1)

int V,E,r,a,b,c;
vector<int> G_t[MAX_V];
vector<int> G_c[MAX_V];

int d[MAX_V];
void dijkstra(){
  int i;
  for(i=0;i<MAX_V;i++)d[i]=INF;
  d[r]=0;
  priority_queue< pair<int,int> > Q;
  Q.push( make_pair(-d[r],r) );
  while(!Q.empty()){
    pair<int ,int > p=Q.top();
    Q.pop();
    int pos=p.second,cost=-p.first;
    if(cost > d[pos] )continue;
    for(i=0;i<G_t[pos].size();i++){
      int to=G_t[pos][i];
      int newcost=cost+G_c[pos][i];
      if(newcost <d[to]){
	d[to]=newcost;
	Q.push( make_pair(-d[to],to) );
      }
    }
  }
  for(i=0;i<V;i++){
    if(d[i]==INF)printf("INF\n");
    else printf("%d\n",d[i]);
  }
}
int main(){
  int i;
  scanf("%d%d%d",&V,&E,&r);
  for(i=0;i<E;i++){
    scanf("%d%d%d",&a,&b,&c);
    G_t[a].push_back(b);
    G_c[a].push_back(c);
  }
  dijkstra();
  return 0;
}