Problem Statement

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.