Pythagorean Triplet Finder

Given an array of integers, you are to determine whether there exists a triplet \(a, b, c\) in the array such that \(a^2 + b^2 = c^2\). This problem involves basic arithmetic and efficient searching. The formula is given as: \(a^2 + b^2 = c^2\). Your task is to read the input data, process the array, and output True if such triplet exists; otherwise, output False.

Note that a triplet consists of three distinct elements (they need not be in any particular order). Ensure that your program reads input from stdin and outputs the result to stdout.

inputFormat

The first line contains an integer \(N\) indicating the number of elements in the array. The second line contains \(N\) space-separated integers representing the array elements.

outputFormat

Output a single line: True if there exists a triplet \(a, b, c\) in the array that satisfies \(a^2 + b^2 = c^2\), otherwise output False.

5
3 1 4 6 5

True