Dolphin is planning to generate a small amount of a certain chemical substance C.
In order to generate the substance C, he must prepare a solution which is a mixture of two substances A and B in the ratio of M_a:M_b.
He does not have any stock of chemicals, however, so he will purchase some chemicals at a local pharmacy.
The pharmacy sells N kinds of chemicals. For each kind of chemical, there is exactly one package of that chemical in stock.
The package of chemical i contains a_i grams of the substance A and b_i grams of the substance B, and is sold for c_i yen (the currency of Japan).
Dolphin will purchase some of these packages. For some reason, he must use all contents of the purchased packages to generate the substance C.
Find the minimum amount of money required to generate the substance C.
If it is not possible to generate the substance C by purchasing any combination of packages at the pharmacy, report that fact.

Constraints

* 1≦N≦40
* 1≦a_i,b_i≦10
* 1≦c_i≦100
* 1≦M_a,M_b≦10
* gcd(M_a,M_b)=1
* a_i, b_i, c_i, M_a and M_b are integers.

Input

The input is given from Standard Input in the following format:


N M_a M_b
a_1 b_1 c_1
a_2 b_2 c_2
:
a_N b_N c_N


Output

Print the minimum amount of money required to generate the substance C. If it is not possible to generate the substance C, print `-1` instead.

Examples

Input

3 1 1
1 2 1
2 1 2
3 3 10


Output

3


Input

1 1 10
10 10 10


Output

-1
import java.util.*; import java.io.*; import java.math.*;
public class Main{
	//Don't have to see. start------------------------------------------
	static class InputIterator{
		ArrayList<String> inputLine = new ArrayList<String>(1024);
		int index = 0; int max; String read;
		InputIterator(){
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			try{
				while((read = br.readLine()) != null){
					inputLine.add(read);
				}
			}catch(IOException e){}
			max = inputLine.size();
		}
		boolean hasNext(){return (index < max);}
		String next(){
			if(hasNext()){
				return inputLine.get(index++);
			}else{
				throw new IndexOutOfBoundsException("There is no more input");
			}
		}
	}
	static HashMap<Integer, String> CONVSTR = new HashMap<Integer, String>();
	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
	static PrintWriter out = new PrintWriter(System.out);
	static void flush(){out.flush();}
	static void myout(Object t){out.println(t);}
	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
	static String next(){return ii.next();}
	static boolean hasNext(){return ii.hasNext();}
	static int nextInt(){return Integer.parseInt(next());}
	static long nextLong(){return Long.parseLong(next());}
	static double nextDouble(){return Double.parseDouble(next());}
	static ArrayList<String> nextStrArray(){return myconv(next(), 8);}
	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
	static ArrayList<Integer> nextIntArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Integer> ret = new ArrayList<Integer>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Integer.parseInt(input.get(i)));
		}
		return ret;
	}
	static ArrayList<Long> nextLongArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Long> ret = new ArrayList<Long>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Long.parseLong(input.get(i)));
		}
		return ret;
	}
	static String myconv(Object list, int no){//only join
		String joinString = CONVSTR.get(no);
		if(list instanceof String[]){
			return String.join(joinString, (String[])list);
		}else if(list instanceof ArrayList){
			return String.join(joinString, (ArrayList)list);
		}else{
			throw new ClassCastException("Don't join");
		}
	}
	static ArrayList<String> myconv(String str, int no){//only split
		String splitString = CONVSTR.get(no);
		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
	}
	public static void main(String[] args){
		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
		solve();flush();
	}
	//Don't have to see. end------------------------------------------
    static void solve(){//Here is the main function
  ArrayList<Integer> one = nextIntArray();
  int N = one.get(0);
  int MA = one.get(1);
  int MB = one.get(2);
  ArrayList[] list = new ArrayList[N];
  int maxValue = 401;
  int[][][] dp = new int[N + 1][maxValue][maxValue];
  for(var i = 0; i < N; i++){
    list[i] = nextIntArray();
  }
  for(var i = 0; i < N + 1; i++){
    for(int j = 0; j < maxValue; j++){
      Arrays.fill(dp[i][j], -1);
    }
  }
      
      
  dp[0][0][0] = 0;
  //dp[i][j][k] : i個目を買い、MA合計がj、MB合計がkになる時の最小コスト
  for(int i = 1; i <= N; i++){
	for(int j = 0; j < maxValue; j++){
		for(int k = 0; k < maxValue; k++){
			if(dp[i - 1][j][k] != -1){
				dp[i][j][k] = dp[i - 1][j][k];
			}
		}
		
	}
    ArrayList<Integer> item = list[i - 1];
    for(int j = 0; j < maxValue; j++){
      for(int k = 0; k < maxValue; k++){
        //myerr({i,j,k});
        if(dp[i - 1][j][k] != -1){
          if(dp[i][j + item.get(0)][k + item.get(1)] == -1){
            dp[i][j + item.get(0)][k + item.get(1)] = dp[i - 1][j][k] + item.get(2);
          }else{
            dp[i][j + item.get(0)][k + item.get(1)] = Math.min(dp[i - 1][j][k] + item.get(2), dp[i][j + item.get(0)][k + item.get(1)]);
          }
        }
      }
    }
  }
	int count = 1;
	int output = 10000;
	while(true){
		int getMA = MA * count;
		int getMB = MB * count;
		if(getMA < maxValue && getMB < maxValue){
			if(dp[N][getMA][getMB] != -1){
				output = Math.min(output,dp[N][getMA][getMB]);
			}
		}else{
			break;
		}
		count++;
	}
	if(output == 10000){
		myout(-1);
	}else{
		myout(output);
	}
      
      
	}
	//Method addition frame start


  
	//Method addition frame end
}
