Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only 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

The problem statement has recently been changed. View the changes.

×
F. New Year and Handle Change

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputNew Year is getting near. So it's time to change handles on codeforces. Mishka wants to change his handle but in such a way that people would not forget who he is.

To make it work, he only allowed to change letters case. More formally, during one handle change he can choose any segment of his handle $$$[i; i + l - 1]$$$ and apply tolower or toupper to all letters of his handle on this segment (more fomally, replace all uppercase letters with corresponding lowercase or vice versa). The length $$$l$$$ is fixed for all changes.

Because it is not allowed to change codeforces handle too often, Mishka can perform at most $$$k$$$ such operations. What is the minimum value of $$$min(lower, upper)$$$ (where $$$lower$$$ is the number of lowercase letters, and $$$upper$$$ is the number of uppercase letters) can be obtained after optimal sequence of changes?

Input

The first line of the input contains three integers $$$n, k$$$ and $$$l$$$ ($$$1 \le n, k, l \le 10^6, l \le n)$$$ — the length of Mishka's handle, the number of changes and the length of the segment.

The second line of the input contains one string $$$s$$$, consisting of $$$n$$$ lowercase and uppercase Latin letters — Mishka's handle.

Output

Print one integer — the minimum value of $$$min(lower, upper)$$$ after that Mishka change his handle at most $$$k$$$ times in a way described in the problem statement.

Examples

Input

7 1 4 PikMike

Output

0

Input

15 2 2 AaAaAAaaAAAAaaA

Output

2

Input

14 2 6 aBcdEFGHIJklMn

Output

0

Input

9 2 2 aAaAAAaaA

Output

1

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/27/2021 16:11:55 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|