B. Level Up
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Being a fan of MMORPGs, Steve was really excited when World of Warcraft Classic was announced. He started playing from the first day and now has only two levels to go till the maximum level. Of course, he doesn't have as much time as he used to have when the game first appeared, so he really wants to finish these two levels as fast as possible.

In order to pass the first level, Steve needs $$$s_1$$$ experience. Only after he gains it, he can move to the second level, in which he needs to get other $$$s_2$$$ experience to pass it.

Steve has the list of $$$n$$$ available quests. He knows that he may finish two levels with these quests. In order to pass the $$$i$$$-th quest, Steve needs $$$t_i$$$ minutes. As a result, he will get $$$x_i$$$ experience for this quest.

When Steve finishes a quest that takes him to the next level, the extra experience overflow is subtracted from the next level's required experience. Once he levels up, all the quests that are left will offer less experience $$$y_i$$$, but they will also require less time $$$r_i$$$.

Note that if Steve finishes a quest, he can't repeat this quest anymore (even in another level).

Given the list of quests, help Steve choose the order in which he will be doing the quests in order to finish the last two levels as fast as possible.

Input

The first line contains three integers $$$n$$$, $$$s_1$$$, $$$s_2$$$ ($$$1 \le n, s_1, s_2 \le 500$$$) — the number of quests, experience required for the first level and experience required for the second level.

Each of the next $$$n$$$ lines contains four integers $$$x_i$$$, $$$t_i$$$, $$$y_i$$$, $$$r_i$$$ ($$$1 \leq y_i < x_i \leq 500$$$, $$$1 \leq r_i < t_i \leq 10^9$$$) where $$$x_i$$$ and $$$y_i$$$ are the experience you will gain from the $$$i$$$-th quest on the $$$1$$$-st and $$$2$$$-nd level respectively and $$$t_i$$$ and $$$r_i$$$ are the number of minutes you need to spend in order to pass this quest on the $$$1$$$-st and $$$2$$$-nd level respectively,

Output

Print one number, representing the minimum number of minutes that Steve needs to finish two levels, or $$$-1$$$ if there is no way to complete quests to finish both levels.

Examples
Input
2 100 100
100 100 10 10
101 11 100 10
Output
110
Input
4 20 20
40 1000 20 20
6 6 5 5
10 10 1 1
10 10 1 1
Output
40
Input
2 20 5
10 10 5 5
10 10 5 5
Output
-1