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<iostream>
#include<queue>
#define INF 1000000000

using namespace std;

struct edge{int to,cost;};
typedef pair<int,int> P;

int v,e,r;
int s[500003],t[500003],c[500003];
int d[100003];
vector<edge> G[500003];

void dijkstra(int s){
  priority_queue<P,vector<P>,greater<P> > que;
  fill(d,d+v,INF);
  d[s]=0;
  que.push(P(0,s));

  while(!que.empty()){
    P p=que.top(); que.pop();
    int u=p.second;
    if(d[u]<p.first) continue;
    for(int i=0;i<G[u].size();i++){
      edge e=G[u][i];
      if(d[e.to]>d[u]+e.cost){
        d[e.to]=d[u]+e.cost;
        que.push(P(d[e.to],e.to));
      }}}}


int main(){
  scanf("%d%d%d",&v,&e,&r);
  for(int i=0;i<e;i++){
    scanf("%d%d%d",&s[i],&t[i],&c[i]);
    edge tmp={t[i],c[i]};
    G[s[i]].push_back(tmp);
  }


  dijkstra(r);

  for(int i=0;i<v;i++){
    if(d[i]==INF) printf("INF\n");
    else printf("%d\n",d[i]);
  }
  return 0;

}