The contest will be held over 5 hours. In these 5 hours you will try and solve as many of the approximately 10 so called problems. You will do this in a team of three people on one computer.
The problems consist of a descriptive text and an example. Every single problem expects an input file which you process and give the correct output file. These problems will be mathematical or algorithmic.
Example: Stand on Zanzibar
Source: BAPC 2015
Turtles live long (and prosper). Turtles on the island Zanzibar are even immortal. Furthermore, they are asexual, and every year they give birth to at most one child. Apart from that, they do nothing. They never leave their tropical paradise.
Zanzi Bar, the first turtle on Zanzibar, has one further activity: it keeps track of the number of turtles on the island. Every New Year’s Day it counts the turtles, and writes the total number in a small booklet. After many years this booklet contains a nondecreasing sequence of integers, starting with one or more ones. (After emerging from its egg on Zanzibar’s beautiful beach, it took Zanzi some time to start a family on its own.)
One day Zanzi realizes that it could also be the case that turtles from abroad come to Zanzibar, by boat or plane. Now it wonders how many of the inhabitants were not born on Zanzibar. Unfortunately, it can only derive a lower bound from the sequence in the booklet. Indeed, if the number of turtles in a year is more than twice as big as the year before, the difference must be fully explained by import.
As soon as Zanzibar has
Input
The input starts with a line containing an integer

One line containing a sequence of spaceseparated, positive integers (
≤1000000 $\le 1\phantom{\rule{thinmathspace}{0ex}}000\phantom{\rule{thinmathspace}{0ex}}000$), nondecreasing, starting with one or more ones. For convenience, a single space and a 0 are appended to the end of the sequence.
Output
For each test case, output a line containing a single integer: the lower bound for the number of turtles not born on Zanzibar.
Sample Input 1  Sample Output 1 

3 1 100 0 1 1 1 2 2 4 8 8 9 0 1 28 72 0 
98 0 42 