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.*;
import java.util.*;

public class Main {
    public static PrintWriter out;
    public static FastScanner in;

    private void solve(){
        int n = in.nextInt();
        int ma = in.nextInt();
        int mb = in.nextInt();

        int[][] dp = new int[401][401];
        for(int i=0;i<=400;i++){
            Arrays.fill(dp[i],Integer.MAX_VALUE);
        }
        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=400-a;j>=0;j--){
                for(int k=400-b;k>=0;k--){
                    if(dp[j][k]!=Integer.MAX_VALUE){
                        dp[j+a][k+b] = Math.min(dp[j+a][k+b],dp[j][k]+c);
                    }
                }
            }
        }
        int mn = Integer.MAX_VALUE;
        for(int i=0;i<=400;i++){
            for(int j=0;j<=400;j++){
                if(dp[i][j]!=Integer.MAX_VALUE){
                    int g = gcd(i,j);
                    if(g == 0) continue;
                    if(i/g == ma && j/g == mb){
                        mn = Math.min(mn,dp[i][j]);
                    }
                }
            }
        }
        if(mn == Integer.MAX_VALUE) out.print(-1);
        else out.print(mn);
    }

    private int gcd(int a ,int b){
        if(b==0) return a;
        return gcd(b,a%b);
    }

    private void runIO() {
        in = new FastScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        solve();
        out.close();
    }
    private static class FastScanner {
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        private FastScanner() {
            bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        }

        private String next() {
            if (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

        private int nextInt() {
            return Integer.parseInt(next());
        }

        private long nextLong() {
            return Long.parseLong(next());
        }

        private String nextLine() {
            String ret = "";
            try {
                ret = bufferedReader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return ret;
        }
    }

    public static void main(String[] args) {
        new Main().runIO();
    }
}
