Sort String by Case and Order

Given an input string s consisting solely of lower-case and upper-case English letters, your task is to rearrange the letters so that:

• All uppercase letters appear first and are sorted in reverse alphabetical order.
• All lowercase letters follow and are sorted in alphabetical order.

For example, if s = "cBaA", then the output should be "BAac".

The formal specification is as follows:

Let \( U = \{ x \in s : x \text{ is uppercase} \} \) and \( L = \{ x \in s : x \text{ is lowercase} \} \). Then, output the string formed by concatenating the elements of \( U \) sorted in descending lexicographical order and the elements of \( L \) sorted in ascending lexicographical order.

inputFormat

The input consists of a single line containing the string s. The string will contain at least 0 and at most 1000 English letters.

Input Format: A single line read from the standard input.

outputFormat

Output the rearranged string according to the problem statement.

Output Format: Print a single line to the standard output.

## sample

cBaA

BAac