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>
using namespace std;

int V,E,R,S[500010],T[500010],D[500010]; //問題で与えられる入力
int C[100000]; //各頂点までの最短距離の上限
//無限を表す定数を全頂点をたどる最大超に設定
const int Inf = 10000*100000+100;

int main(){
  for (int i = 0; i < 100000; i++){
   C[i] = Inf;
   }
  cin >> V >> E >> R;
  C[R] = 0;
  for (int i=0; i<E; i++){
    cin >> S[i] >> T[i] >> D[i]; //各辺を入力
	//Cを初期化:C[R]を0に、他をInfに
	}
	for (int t=0; t<V; ++t) { //V回繰り返す
	  bool update = false;
	  for (int i = 0; i<E; ++i) {
	    int s = S[i], t = T[i], d = D[i]; //i番目の辺のs,t,dに対して
		if (C[s] < Inf && C[t] > C[s] + d) { //辺s,tで緩和できるなら
		  C[t] = C[s] + d;//C[t]を更新
		  update = true; //更新が起こったことを記録
		  }
		 }
		if (!update) break; //辺を一巡して更新がなければ打ち切ってよい
		}
	   for (int j=0; j < V; j++){
	    if (C[j] < Inf){
	    cout << C[j] << endl;
		}
		else {
		cout << "INF" << endl;
		}
	  }
	}