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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

class Solver {
  final int n;
  final long[] as;
  
  Solver(int n, long[] as) {
    this.n = n;
    this.as = as;
  }
  
  private long calculate(int positiveIndex) {
//    System.err.printf("positiveIndex: %d\n", positiveIndex);
    long answer = 0;
    {
      long prevShift = 0;
      for (int i = positiveIndex + 1; i < n; i++) {
        long shift = prevShift;
        if (as[i - 1] < as[i]) {
          for (int j = 1; shift >= 2 && (as[i - 1] << (2 * j)) <= as[i]; j++) {
            shift -= 2;
          }
        } else {
          for (int j = 0; as[i - 1] > (as[i] << (2 * j)); j++) {
            shift += 2;
          }
        }
//        System.err.printf("p i: %d, shift: %d\n", i, shift);
        answer += shift;
        prevShift = shift;
      }
    }
    
    {
      answer += positiveIndex;
      long prevShift = 0;
      for (int i = positiveIndex - 2; i >= 0; i--) {
        long shift = prevShift;
        if (as[i] < as[i + 1]) {
          for (int j = 1; shift >= 2 && (as[i] << (2 * j)) <= as[i + 1]; j++) {
            shift -= 2;
          }
        } else {
          for (int j = 0; as[i] > (as[i + 1] << (2 * j)); j++) {
            shift += 2;
          }
        }
//        System.err.printf("n i: %d, shift: %d\n", i, shift);
        answer += shift;
        prevShift = shift;
      }
    }
//    System.err.println(answer);
//    System.err.println();
    return answer;
  }
  
  public long solve() {
    int minPositiveIndex = 0;
    int maxPositiveIndex = n;
    while (maxPositiveIndex - minPositiveIndex >= 3) {
      int mid1PositiveIndex = (2 * maxPositiveIndex + 1 * minPositiveIndex) / 3;
      int mid2PositiveIndex = (1 * maxPositiveIndex + 2 * minPositiveIndex) / 3;
      long mid1Cost = calculate(mid1PositiveIndex);
      long mid2Cost = calculate(mid2PositiveIndex);
      if (mid1Cost <= mid2Cost) {
        minPositiveIndex = mid2PositiveIndex;
      } else {
        maxPositiveIndex = mid1PositiveIndex;
      }
    }
    long answer = Long.MAX_VALUE;
    for (int i = minPositiveIndex; i <= maxPositiveIndex; i++) {
      answer = Math.min(answer, calculate(i));
    }
    return answer;
  }
}

public class Main {
  private static void execute(ContestReader reader, PrintWriter out) {
    int n = reader.nextInt();
    long[] as = reader.nextLong(n);
    out.println(new Solver(n, as).solve());
  }
  
  public static void main(String[] args) {
    ContestReader reader = new ContestReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    execute(reader, out);
    out.flush();
  }
}

class ContestReader {
  private BufferedReader reader;
  private StringTokenizer tokenizer;
  
  ContestReader(InputStream in) {
    reader = new BufferedReader(new InputStreamReader(in));
  }
  
  public String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }
  
  public int nextInt() {
    return Integer.parseInt(next());
  }
  
  public long nextLong() {
    return Long.parseLong(next());
  }
  
  public double nextDouble() {
    return Double.parseDouble(next());
  }
  
  public String[] next(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = next();
    }
    return array;
  }
  
  public int[] nextInt(int n) {
    int[] array = new int[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextInt();
    }
    return array;
  }
  
  public long[] nextLong(int n) {
    long[] array = new long[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLong();
    }
    return array;
  }
  
  public double[] nextDouble(int n) {
    double[] array = new double[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextDouble();
    }
    return array;
  }
  
  public char[] nextCharArray() {
    return next().toCharArray();
  }
  
  public int[][] nextInt(int n, int m) {
    int[][] matrix = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextInt();
      }
    }
    return matrix;
  }
  
  public long[][] nextLong(int n, int m) {
    long[][] matrix = new long[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextLong();
      }
    }
    return matrix;
  }
  
  public double[][] nextDouble(int n, int m) {
    double[][] matrix = new double[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextDouble();
      }
    }
    return matrix;
  }
  
  public char[][] nextCharArray(int n) {
    char[][] matrix = new char[n][];
    for (int i = 0; i < n; i++) {
      matrix[i] = next().toCharArray();
    }
    return matrix;
  }
}