Sort Strings by Length

You are given a list of strings. Your task is to sort the list according to the following rules:

• First, sort by the length of the strings in descending order.
• If two strings have the same length, sort them in lexicographical ascending order.

Mathematically, for two strings \(a\) and \(b\), the comparator can be defined as:

\[ \text{Compare}(a, b) = \begin{cases} -1, & \text{if } |a| > |b| \\ \text{lexicographical comparison}, & \text{if } |a| = |b| \\ 1, & \text{if } |a| < |b| \end{cases} \]

For example, if the input strings are "apple", "orange", "fig", "pineapple", "lime", then the correct output is:

pineapple orange apple lime fig

inputFormat

The input is read from stdin in the following format:

1. The first line contains an integer \(n\) indicating the number of strings.
2. The following \(n\) lines each contain one string.

outputFormat

Output the sorted list of strings in a single line to stdout, with each string separated by a single space.

## sample

5
apple
orange
fig
pineapple
lime

pineapple orange apple lime fig