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
/**
 * Created at 16:45 on 2019-09-04
 */

import java.io.*;
import java.util.*;

public class Main {

  static FastScanner sc = new FastScanner();
  static Output out = new Output(System.out);

  static final int[] dx = {0, 1, 0, -1};
  static final int[] dy = {-1, 0, 1, 0};

  static final long MOD = (long) (1e9 + 7);
  static final long INF = Long.MAX_VALUE / 2;

  static final int e5 = (int) 1e5;

  public static class Solver {
    public Solver() {

      int N = sc.nextInt();
      int Ma = sc.nextInt();
      int Mb = sc.nextInt();

      Triplet[] tri = new Triplet[N];
      for (int i=0; i<N; i++) {
        tri[i] = new Triplet(sc.nextInt(), sc.nextInt(), sc.nextInt());
      }

      long[][][] dp = new long[N+1][401][401];
      for (int i=0; i<=N; i++) {
        for (int j=0; j<=400; j++) {
          Arrays.fill(dp[i][j], INF);
        }
      }
      dp[0][0][0] = 0;
      for (int i=1; i<=N; i++) {
        for (int j=0; j<=400; j++) {
          for (int k=0; k<=400; k++) {

            if (j-tri[i-1].a >= 0 && k-tri[i-1].b >= 0) {
              dp[i][j][k] = Math.min(dp[i - 1][j][k], dp[i - 1][j - tri[i-1].a][k - tri[i-1].b] + tri[i-1].c);
            } else {
              dp[i][j][k] = dp[i-1][j][k];
            }

          }
        }
      }

      long ans = INF;
      for (int t=1; ;t++) {
        if (Ma*t > 400 || Mb*t > 400) break;
        ans = Math.min(ans, dp[N][Ma*t][Mb*t]);
      }

      out.println(ans == INF ? -1 : ans);

    }

    class Triplet {
      int a, b, c;
      Triplet(int A, int B, int C) {
        a = A;
        b = B;
        c = C;
      }
    }
  }

  public static void main(String[] args) {
    new Solver();
    out.flush();
  }

  static class FastScanner {
    private InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;


    public void load() {
      try {
        in = new FileInputStream(next());
      } catch (Exception e) {
        e.printStackTrace();
      }
    }

    private boolean hasNextByte() {
      if (ptr < buflen) {
        return true;
      } else {
        ptr = 0;
        try {
          buflen = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (buflen <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    public boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    public long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public int[] nextIntArray(int N, boolean oneBased) {
      if (oneBased) {
        int[] array = new int[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      } else {
        int[] array = new int[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      }
    }

    public long[] nextLongArray(int N, boolean oneBased) {
      if (oneBased) {
        long[] array = new long[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      } else {
        long[] array = new long[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      }
    }
  }

  static class Output extends PrintWriter {

    private long startTime;

    public Output(PrintStream ps) {
      super(ps);
    }

    public void print(int[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(long[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(String[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(ArrayList a, String separator) {
      for (int i = 0; i < a.size(); i++) {
        if (i == 0) print(a.get(i));
        else print(separator + a.get(i));
      }
      println();
    }

    public void start() {
      startTime = System.currentTimeMillis();
    }

    public void time(String s) {
      long time = System.currentTimeMillis() - startTime;
      println(s + "(" + time + ")");
    }

  }

}
