# Problem G

Tall Towers

You are very well aware of the saying “When life gives you blocks, make towers!”. So, you decide to do exactly that.

You have $n$ blocks of size $l_ i \times w_ i \times 1$ (that is, the height of each block is 1 unit). You want to completely use up all these blocks such that the average height of towers is as high as possible. Towers are made in the usual way: by stacking up blocks one on top of the other.

Of course, you have an eye for beauty, so just any random stack of blocks does not count as a tower for you. For every block in a tower (except the bottom-most block), you wish to ensure that it is “just the right amount” smaller than the block below it. More precisely, you can put block j on top of block k if and only if $x \cdot l_ k \leq l_ j \leq y \cdot l_ k$ and $x \cdot w_ k \leq w_ j \leq y \cdot w_ k$. You are guaranteed that $ 0 < x \leq y < 1 $.

## Input

The first line of the input contains three space separated positive integers: the number of blocks $n$ ($1\leq n \leq 200 $), $x\prime $ ($1\leq x\prime < 10^6 $), and $y\prime $ ($1\leq y\prime < 10^6 $) where $x = \frac{x\prime }{10^6}$ and $y = \frac{y\prime }{10^6}$. You are guaranteed that $ x \leq y $. Then follow $n$ lines, each describing a block. The $i^{th}$ line contains two space separated positive integers $l_ i$ and $w_ i$ corresponding to the length and width of the $i^{th}$ block. You are guaranteed that $ 1 \leq l_ i, w_ i \leq 10^9$.

## Output

Print a single integer, the number of towers in an arrangement of blocks that maximizes the average height of the towers. It can be proven that the answer is unique.

Sample Input 1 | Sample Output 1 |
---|---|

2 1 999999 5 4 1 3 |
1 |

Sample Input 2 | Sample Output 2 |
---|---|

8 1 999999 1 16 2 15 3 14 4 13 5 12 6 11 7 10 8 9 |
8 |

Sample Input 3 | Sample Output 3 |
---|---|

8 500000 500000 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 |
4 |