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<algorithm>
#include<vector>
#include<queue>
using namespace std;

typedef pair<int,int> pii;

struct edge{int to,cost;};
const int INF = 1000000000;
const int MAX_V = 100000;

int main(){
  int V,E,r;
  int d[MAX_V];
  vector<edge> G[MAX_V];
  priority_queue<pii,vector<pii>,greater<pii> > q;
  scanf("%d %d %d",&V,&E,&r);
  for(int i=0;i<E;i++){
    int s,t,d;
    scanf("%d %d %d",&s,&t,&d);
    edge e;
    e.cost = d; e.to = t;
    G[s].push_back(e);
  }
  fill(d,d+V,INF);
  d[r] = 0;
  q.push(pii(0,r));

  while(!q.empty()){
    pii p = q.top(); q.pop();
    int v = p.second;
    if(p.first>d[v]) continue;
    for(int i=0;i<G[v].size();i++){
      if(d[G[v][i].to]>d[v]+G[v][i].cost){
        d[G[v][i].to] = d[v] + G[v][i].cost;
        q.push(pii(d[G[v][i].to],G[v][i].to));
      }
    }
  }
  for(int i=0;i<V;i++){
    if(d[i]==INF) printf("INF\n");
    else printf("%d\n",d[i]);
  }
  return 0;
}