The Viral Coefficient

One of Meridian's drinks was picked up by a food blogger, and the owner wants to know how often the story genuinely caught fire rather than merely grew. A day catches fire if it sold at least twice what the day before it sold, and a day that lands on exactly double counts.

Task: Print how many days at least doubled on the day before them.

Input

The first line holds an integer n, always at least 2. Each of the next n lines holds one day's order count, always greater than zero.

Output

One line: a whole number between 0 and n - 1. The opening day has nothing before it and can never count. Print 0 when no day doubled.

Example:

Input:
4
5
12
20
50

Output:
2