B. Power Sequencetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLet's call a list of positive integers a_0, a_1, ..., a_{n-1} a power sequence if there is a positive integer c, so that for every 0 \le i \le n-1 then a_i = c^i.Given a list of n positive integers a_0, a_1, ..., a_{n-1}, you are allowed to:  Reorder the list (i.e. pick a permutation p of \{0,1,...,n - 1\} and change a_i to a_{p_i}), then  Do the following operation any number of times: pick an index i and change a_i to a_i - 1 or a_i + 1 (i.e. increment or decrement a_i by 1) with a cost of 1. Find the minimum cost to transform a_0, a_1, ..., a_{n-1} into a power sequence.InputThe first line contains an integer n (3 \le n \le 10^5).The second line contains n integers a_0, a_1, ..., a_{n-1} (1 \le a_i \le 10^9).OutputPrint the minimum cost to transform a_0, a_1, ..., a_{n-1} into a power sequence.ExamplesInput
3
1 3 2
Output
1
Input
3
1000000000 1000000000 1000000000
Output
1999982505
NoteIn the first example, we first reorder \{1, 3, 2\} into \{1, 2, 3\}, then increment a_2 to 4 with cost 1 to get a power sequence \{1, 2, 4\}.
3
1 3 2

1 
['brute force', 'math', 'number theory', 'sortings', '*1500']