Prime Factorization

You are given a positive integer \(n\). Your task is to compute its prime factorization and print the result as a dictionary in the following format:

{prime1: exponent1, prime2: exponent2, ...}

The dictionary should list prime factors in increasing order. For example, when \(n = 18\), the prime factorization is \(2^1 \times 3^2\), so the output should be {2: 1, 3: 2}.

Note: You must read the input from stdin and print the result to stdout.

inputFormat

The input consists of a single line containing an integer \(n\) \((n \ge 2)\).

outputFormat

Output the prime factors of \(n\) in a dictionary format with keys in increasing order. There should be no extra spaces except those shown in the examples.

For example:

{2: 1, 3: 2}

18

{2: 1, 3: 2}