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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;

public class Main implements Runnable {
    static ContestScanner in;
    static Writer out;
    public static void main(String[] args) {
        new Thread(null, new Main(), "", 16 * 1024 * 1024).start();
    }

    public void run() {
        Main main = new Main();
        try {
            in = new ContestScanner();
            out = new Writer();
            main.solve();
            out.close();
            in.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }


    void solve() throws IOException {
        int n = in.nextInt();
        int ma = in.nextInt();
        int mb = in.nextInt();
        int dpsize = n * 10 + 1;
        int[][] dp = new int[dpsize][dpsize];
        int inf = Integer.MAX_VALUE / 2;
        for (int i = 0; i < dpsize; i++) {
            Arrays.fill(dp[i], inf);
        }
        dp[0][0] = 0;
        for(int i = 0; i < n; i++) {
            int a = in.nextInt();
            int b = in.nextInt();
            int c = in.nextInt();
            for (int j = dpsize - 1; j >= 0; j--) {
                for (int k = dpsize - 1; k >= 0; k--) {
                    if(dp[j][k] == inf) continue;
                    dp[j + a][k + b] = Math.min(dp[j + a][k + b],
                            dp[j][k] + c);
                }
            }
        }
        int ans = inf;
        for (int i = 1; i < dpsize; i++) {
            if(i % ma != 0) continue;
            for (int j = 1; j < dpsize; j++) {
                if(j % mb != 0 || j / mb != i / ma) continue;
                ans = Math.min(ans, dp[i][j]);
            }
        }
        if(ans == inf) ans = -1;
        System.out.println(ans);
    }
}

@SuppressWarnings("serial")
class MultiSet<T> extends HashMap<T, Integer>{
    @Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
    public void add(T key,int v){put(key,get(key)+v);}
    public void add(T key){put(key,get(key)+1);}
    public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
    public MultiSet<T> merge(MultiSet<T> set)
    {MultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
        for(Entry<T,Integer>e:s.entrySet())l.add(e.getKey(),e.getValue());return l;}
}

class Writer extends PrintWriter{
    public Writer(String filename)throws IOException
    {super(new BufferedWriter(new FileWriter(filename)));}
    public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
    private BufferedReader in;private int c=-2;
    public ContestScanner()throws IOException
    {in=new BufferedReader(new InputStreamReader(System.in));}
    public ContestScanner(String filename)throws IOException
    {in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
    public String nextToken()throws IOException {
        StringBuilder sb=new StringBuilder();
        while((c=in.read())!=-1&&Character.isWhitespace(c));
        while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public String readLine()throws IOException{
        StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
        while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public long nextLong()throws IOException,NumberFormatException
    {return Long.parseLong(nextToken());}
    public int nextInt()throws NumberFormatException,IOException
    {return(int)nextLong();}
    public double nextDouble()throws NumberFormatException,IOException
    {return Double.parseDouble(nextToken());}
    public void close() throws IOException {in.close();}
}