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This round has an unusual addition to the rules. For each problem you must use distinct language. Thus, if you have a submission that has passed at least one test or is being tested at the moment, then for this task you can use only this language and can not use it for other tasks. More details can be read by the link. Different implementations of the same language are considered to be the same language (for example, in C++ you can only solve one problem, regardless of the exact chosen compiler).

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A. Amusement Park

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPupils decided to go to amusement park. Some of them were with parents. In total, *n* people came to the park and they all want to get to the most extreme attraction and roll on it exactly once.

Tickets for group of *x* people are sold on the attraction, there should be at least one adult in each group (it is possible that the group consists of one adult). The ticket price for such group is *c*_{1} + *c*_{2}·(*x* - 1)^{2} (in particular, if the group consists of one person, then the price is *c*_{1}).

All pupils who came to the park and their parents decided to split into groups in such a way that each visitor join exactly one group, and the total price of visiting the most extreme attraction is as low as possible. You are to determine this minimum possible total price. There should be at least one adult in each group.

Input

The first line contains three integers *n*, *c*_{1} and *c*_{2} (1 ≤ *n* ≤ 200 000, 1 ≤ *c*_{1}, *c*_{2} ≤ 10^{7}) — the number of visitors and parameters for determining the ticket prices for a group.

The second line contains the string of length *n*, which consists of zeros and ones. If the *i*-th symbol of the string is zero, then the *i*-th visitor is a pupil, otherwise the *i*-th person is an adult. It is guaranteed that there is at least one adult. It is possible that there are no pupils.

Output

Print the minimum price of visiting the most extreme attraction for all pupils and their parents. Each of them should roll on the attraction exactly once.

Examples

Input

3 4 1

011

Output

8

Input

4 7 2

1101

Output

18

Note

In the first test one group of three people should go to the attraction. Then they have to pay 4 + 1 * (3 - 1)^{2} = 8.

In the second test it is better to go to the attraction in two groups. The first group should consist of two adults (for example, the first and the second person), the second should consist of one pupil and one adult (the third and the fourth person). Then each group will have a size of two and for each the price of ticket is 7 + 2 * (2 - 1)^{2} = 9. Thus, the total price for two groups is 18.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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