Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

F. Fence

time limit per test

2 secondsmemory limit per test

256 megabytesinput

input.txtoutput

output.txtVasya should paint a fence in front of his own cottage. The fence is a sequence of *n* wooden boards arranged in a single row. Each board is a 1 centimeter wide rectangle. Let's number the board fence using numbers 1, 2, ..., *n* from left to right. The height of the *i*-th board is *h*_{i} centimeters.

Vasya has a 1 centimeter wide brush and the paint of two colors, red and green. Of course, the amount of the paint is limited. Vasya counted the area he can paint each of the colors. It turned out that he can not paint over *a* square centimeters of the fence red, and he can not paint over *b* square centimeters green. Each board of the fence should be painted exactly one of the two colors. Perhaps Vasya won't need one of the colors.

In addition, Vasya wants his fence to look smart. To do this, he should paint the fence so as to minimize the value that Vasya called the fence unattractiveness value. Vasya believes that two consecutive fence boards, painted different colors, look unattractive. The unattractiveness value of a fence is the total length of contact between the neighboring boards of various colors. To make the fence look nice, you need to minimize the value as low as possible. Your task is to find what is the minimum unattractiveness Vasya can get, if he paints his fence completely.

The picture shows the fence, where the heights of boards (from left to right) are 2,3,2,4,3,1. The first and the fifth boards are painted red, the others are painted green. The first and the second boards have contact length 2, the fourth and fifth boards have contact length 3, the fifth and the sixth have contact length 1. Therefore, the unattractiveness of the given painted fence is 2+3+1=6.

Input

The first line contains a single integer *n* (1 ≤ *n* ≤ 200) — the number of boards in Vasya's fence.

The second line contains two integers *a* and *b* (0 ≤ *a*, *b* ≤ 4·10^{4}) — the area that can be painted red and the area that can be painted green, correspondingly.

The third line contains a sequence of *n* integers *h*_{1}, *h*_{2}, ..., *h*_{n} (1 ≤ *h*_{i} ≤ 200) — the heights of the fence boards.

All numbers in the lines are separated by single spaces.

Output

Print a single number — the minimum unattractiveness value Vasya can get if he paints his fence completely. If it is impossible to do, print - 1.

Examples

Input

4

5 7

3 3 4 1

Output

3

Input

3

2 3

1 3 1

Output

2

Input

3

3 3

2 2 2

Output

-1

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/24/2017 10:27:07 (c2).

Desktop version, switch to mobile version.
User lists

Name |
---|