A strange object has fallen from space onto Alpha Planet! M inhabitants of Alpha Planet have gathered around the object, which looks like a string of length N. Since the inhabitants like palindromes a lot, they want to partition the object into M different pieces such that each inhabitant gets a palindrome. In other words, they want to split the string into M non-overlapping substrings, of which all are palindromes.

They have a special tool that allows them to change characters of the object. Each use of the tool changes 1 character of the object, and the tool can be used up to X times. They want to know whether or not it is possible for each inhabitant to get a palindrome, if they use their special tool up to X times. If it is possible, they also want to know the minimum number of times they need to use the special tool, as it is quite expensive to operate the tool.

A palindrome is a word that is equal to itself when reversed. For example, “program” is not a palindrome while “deed” is. A single letter is a palindrome too.

Constraints:

• 1 <= M <= N <= 100
• 0 <= X <= 20

Input Format:

• First line of input gives the numbers N, M, X, the length of the string, number of inhabitants, and the maximum number of uses of the special tool, respectively
• Second line of input gives the string, consisted of only lowercase letters

Output Format:

• Output “NO” (without quotes) if it is not possible to for every inhabitant to get a palindrome, even after using the tool up to X times
• If it is possible, output “YES” (without quotes) on the first line and the minimum number of uses of the special tool on the second line

Examples:

3 2 1
abc

YES
1

5 2 1
abcde

NO

5 3 2
abcde

YES
1

(Problem credit: Justin Li)