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<bits/stdc++.h>
 
#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
 
using namespace std;
 
typedef pair<int,int> ii;
const int IINF = INT_MAX;
 
vector<ii> G[100010];
int mincost[100010];
int V,E,r;
 
int main(){
  scanf("%d %d %d",&V,&E,&r);
 
  int s,t,d;
  rep(i,E){
    scanf("%d %d %d",&s,&t,&d);
    G[s].push_back(ii(t,d));
  }
 
  rep(i,V) mincost[i] = IINF;
  mincost[r] = 0;
  deque<int> deq; deq.push_back(r);
  vector<int> in_queue(V,0); in_queue[r] = 1;
 
  while(!deq.empty()){
    int u = deq.front(); deq.pop_front(); in_queue[u] = 0;
    rep(i,(int)G[u].size()){
      int v = G[u][i].first, c = G[u][i].second;
      if( mincost[v] > mincost[u] + c ) {
        mincost[v] = mincost[u] + c;
        if( !in_queue[v] ) {
          deq.push_back(v);
          in_queue[v] = 1;
        }
      }
    }
  }
 
  rep(i,V) {
    if( mincost[i] == IINF ) puts("INF");
    else printf("%d\n",mincost[i]);
  }
 
  return 0;
}