Score : $400$ points

Problem Statement

A shop sells $N$ kinds of lunchboxes, one for each kind. For each $i = 1, 2, \ldots, N$, the $i$-th kind of lunchbox contains $A_i$ takoyaki (octopus balls) and $B_i$ taiyaki (fish-shaped cakes).

Takahashi wants to eat $X$ or more takoyaki and $Y$ or more taiyaki. Determine whether it is possible to buy some number of lunchboxes to get at least $X$ takoyaki and at least $Y$ taiyaki. If it is possible, find the minimum number of lunchboxes that Takahashi must buy to get them.

Note that just one lunchbox is in stock for each kind; you cannot buy two or more lunchboxes of the same kind.

Constraints

• $1 \leq N \leq 300$
• $1 \leq X, Y \leq 300$
• $1 \leq A_i, B_i \leq 300$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$X$ $Y$

$A_1$ $B_1$

$A_2$ $B_2$

$\vdots$

$A_N$ $B_N$

Output

If Takahashi cannot get at least $X$ takoyaki and at least $Y$ taiyaki, print $-1$; otherwise, print the minimum number of lunchboxes that he must buy to get them.

3
5 6
2 1
3 4
2 3

2

He wants to eat $5$ or more takoyaki and $6$ or more taiyaki. Buying the second and third lunchboxes will get him $3 + 2 = 5$ taiyaki and $4 + 3 = 7$ taiyaki.

3
8 8
3 4
2 3
2 1

-1

Even if he is to buy every lunchbox, it is impossible to get at least $8$ takoyaki and at least $8$ taiyaki. Thus, print $-1$.