National Olympiad in Informatics, China, 2001
The inverse tangent function can be expressed as an infinite series, as shown below:
It is commonly known that the inverse tangent function can be used to compute . For example, an easy way to compute is using the method:
Of course, this method is rather inefficient. We can apply the tangent angle sum identity:
After some simple manipulation, the following is obtained:
Using this identity, let and , then . Therefore:
Using the inverse tangents of and to calculate , the speed is drastically improved.
We take equation (4) and write it in the following form:
where , , and are each positive integers.
The problem is, for a given , find the value of . It is guaranteed that for any there will always exist an integer solution. If there are multiple solutions, you are required to find the minimum value of .
Input Specification
The input consists of a single positive integer , where .
Output Specification
The output should contain a single integer, the value of .
Sample Input
1
Sample Output
5
Problem translated to English by .
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