$A$, $B$, and $C$ are three friends. Their birth dates are in the ratio of $1:2:4$. $B$ forms a quadratic equation of the form $ax^2+bx+c$, where the coefficient $a,b$, and $c$ are the birth date ratios, that is, $a=1$, $b=2$, and $c=4$. 

$C$ is preparing for a test, he gives $n$ online tests and stores the score of these $n$ tests in the form of an array. $C$ wants to arrange the scores of these $n$ tests in a non-decreasing order such that he can show it to his friends about his improvement. He uses the following operation to perform this task: 

• Select one of the test marks and multiply it with the root of the quadratic equation provided by $B$.

Determine the minimum number of operations required to perform the task. 

Input format

• First line: $n$ denoting the number of test cases
• Second line: $n$ integers denoting the marks obtained in each test

Output format

Print a single integer that represents the minimum number of operations that can be performed to complete the task. If it is not possible, then print $-1$.

Constraints

$1 \le n \le 200000\\ 1 \le A_i \le 1e^9$