Arithmetic Progression Triplet

Given an array of integers, determine if there exists a triplet that forms an arithmetic progression. In other words, check whether there exist indices i, j, and k (with i < j < k) such that:

\(a[j] - a[i] = a[k] - a[j]\)

The array elements can be arranged in any order. You are required to read the array from the standard input and print either True (if such a triplet exists) or False (if it does not).

Note: Even if the numbers are not originally sorted, you may sort them before processing.

inputFormat

The first line contains a single integer n, representing the number of elements in the array.

The second line contains n space-separated integers representing the elements of the array.

You should read from standard input (stdin).

outputFormat

Output a single line: True if there exists an arithmetic progression triplet in the array, otherwise False.

The output should be printed to standard output (stdout).

## sample

5
1 3 5 7 9

True