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: Time Limit Exceeded)

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
gapl = []
1.upto(n-2) { |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

    prev = i
    dif = 0
    (gapl.size-1).downto(0) { |j|
      pos = gapl[j][0]
      dex = [gapl[j][1], ex].min
      dif += ex * (prev - pos)
      ex -= dex
      gapl[j][1] -= dex
      prev = pos
      if DBG
        puts "== ij #{i},#{j} pos:#{pos} dex #{dex} dif #{dif}"
        puts "   gapl[j][1] #{gapl[j][1]} prev #{prev} ex #{ex}"
      end
    }
    dif += ex * prev
    tol[i] += dif
  elsif a[i-1] >= 4*a[i]
    ex = -2
    y = a[i-1]
    x = a[i]
    while x <= y
      x *= 4
      ex += 2
    end
    gapl << [i, ex]
    puts "[#{i}, #{ex}] added to gapl" if DBG
  end
}
if DBG
  print "tol:"
  print tol
  puts ""
  print "gapl:"
  print gapl
  puts ""
end

tor[n-1] = 0
gapr = []
(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

    prev = i
    dif = 0
    (gapr.size-1).downto(0) { |j|
      pos = gapr[j][0]
      dex = [gapr[j][1], ex].min
      dif += ex * (pos - prev)
      puts "dif+ #{dif} ex #{ex} pos #{pos} prev #{prev}" if DBG
      ex -= dex
      gapr[j][1] -= dex
      prev = pos
    }
    dif += ex * (n - prev - 1)
    puts "dif+ #{dif} ex #{ex} n #{n} prev #{prev}" if DBG
    tor[i] += dif
  elsif 4*a[i] <= a[i+1]
    ex = -2
    x = a[i]
    y = a[i+1]
    while x <= y
      x *= 4
      ex += 2
    end
    gapr << [i, ex]
    puts "[#{i}, #{ex}] added to gapr" if DBG
  end
}
if DBG
  print "tor:"
  print tor
  puts ""
  print "gapr:"
  print gapr
  puts ""
end

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