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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;

public class Main {
	static final int INF = (int)1e9 + 7;
	int N,Ma,Mb;
	int[] A,B,C;

	public void solve() {
		N = nextInt();
		Ma = nextInt();
		Mb = nextInt();

		A = new int[N];
		B = new int[N];
		C = new int[N];

		for(int i = 0;i < N;i++){
			A[i] = nextInt();
			B[i] = nextInt();
			C[i] = nextInt();
		}

		int[][][] dp = new int[N+1][1010][1010];
		for(int i = 0;i < N + 1;i++){
			for(int j = 0;j < 1010;j++){
				for(int k = 0;k < 1010;k++){
					dp[i][j][k] = INF;
				}
			}
		}

		dp[0][0][0] = 0;
		for(int i = 0;i < N;i++){
			for(int j = 0;j < 1010 - A[i];j++){
				for(int k = 0;k < 1010 - B[i];k++){
					int a = j + A[i];
					int b = k + B[i];
					dp[i+1][j][k] = Math.min(dp[i+1][j][k], dp[i][j][k]);
					dp[i+1][a][b] = Math.min(dp[i+1][a][b],dp[i][j][k]+C[i]);
				}
			}
		}

		int ans = INF;
		int max = Math.max(Ma,Mb);

		for(int i = 1;i * max < 1010;i++){
			ans = Math.min(ans,dp[N][i*Ma][i*Mb]);
		}
		if(ans == INF){
			out.println(-1);
		}else{
			out.println(ans);
		}
	}

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

	/* Input */
	private static final InputStream in = System.in;
	private static final PrintWriter out = new PrintWriter(System.out);
	private final byte[] buffer = new byte[2048];
	private int p = 0;
	private int buflen = 0;

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

	public boolean hasNext() {
		while (hasNextByte() && !isPrint(buffer[p])) {
			p++;
		}
		return hasNextByte();
	}

	private boolean isPrint(int ch) {
		if (ch >= '!' && ch <= '~')
			return true;
		return false;
	}

	private int nextByte() {
		if (!hasNextByte())
			return -1;
		return buffer[p++];
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = -1;
		while (isPrint((b = nextByte()))) {
			sb.appendCodePoint(b);
		}
		return sb.toString();
	}

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

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

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}