Prime Factorization

Given a positive integer \(n\), compute its prime factorization. Express \(n\) as \(n = \prod_{i=1}^{k} p_i^{e_i}\), where each \(p_i\) is a prime number and \(e_i\) is its exponent. The result should be output as a list of tuples in the form (prime, exponent), sorted in increasing order of the prime numbers.

For example, if \(n = 28\), the output should be [(2, 2), (7, 1)].

inputFormat

The input is a single integer \(n\) (where \(n \ge 1\)), provided via standard input.

outputFormat

Output the prime factorization of \(n\) as a list of tuples, where each tuple contains a prime factor and its exponent. The format must exactly match the example output, and the output should be written to standard output.

28

[(2, 2), (7, 1)]