B. Power Sequence
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Let'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.

Input

The first line contains an integer $$$n$$$ ($$$3 \le n \le 10^5$$$).

The second line contains $$$n$$$ integers $$$a_0, a_1, ..., a_{n-1}$$$ ($$$1 \le a_i \le 10^9$$$).

Output

Print the minimum cost to transform $$$a_0, a_1, ..., a_{n-1}$$$ into a power sequence.

Examples
Input
3
1 3 2
Output
1
Input
3
1000000000 1000000000 1000000000
Output
1999982505
Note

In 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 $$$\{1, 2, 4\}$$$.