Problem:
Score : 800 points

Problem Statement

There are N positive integers A_1, A_2, ..., A_N.
Takahashi can perform the following operation on these integers any number of times:

Choose 1 \leq i \leq N and multiply the value of A_i by -2.

Notice that he multiplies it by minus two.

He would like to make A_1 \leq A_2 \leq ... \leq A_N holds.
Find the minimum number of operations required. If it is impossible, print -1.

Constraints

1 \leq N \leq 200000

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the answer.

Sample Input 1

4
3 1 4 1

Sample Output 1

3

One possible solution is:

Choose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now 3, 1, 4, -2.

Choose i=1 and multiply the value of A_1 by -2. A_1, A_2, A_3, A_4 are now -6, 1, 4, -2.

Choose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now -6, 1, 4, 4.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

0

A_1 \leq A_2 \leq ... \leq A_N holds before any operation is performed.

Sample Input 3

8
657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097

Sample Output 3

7

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

DBG = !true
n = gets.to_i
a = gets.split.map{|z| z.to_i}
tol = Array.new(n)
tor = Array.new(n)
tol[0] = 1
1.upto(n-1) { |i|
  tol[i] = 1 + tol[i-1]
  if a[i-1] < a[i]
    ex = 0
    x = a[i-1]
    y = a[i]
    while x < y
      x *= 4
      ex += 2
    end
    tol[i] += ex * i
  end
}
print tol if DBG
puts "" if DBG

tor[n-1] = 0
(n-2).downto(0) { |i|
  tor[i] = tor[i+1]
  if a[i] > a[i+1]
    ex = 0
    x = a[i+1]
    y = a[i]
    while x < y
      x *= 4
      ex += 2
    end
    tor[i] += ex * (n-i-1)
  end
}
print tor if DBG
puts "" if DBG

mn = [tor[0], tol[n-1]].min
for i in 1..(n-1)
  s = tol[i-1] + tor[i]
  mn = s if s < mn
end
print mn