A. Candies and Two Sisters
math
There are two sisters Alice and Betty. You have \(n\) candies. You want to distribute these \(n\) candies between two sisters in such a way that: Alice will get \(a\) (\(a > 0\)) candies; Betty will get \(b\) (\(b > 0\)) candies; each sister will get some integer number of candies; Alice will get a greater amount of candies than Betty (i.e. \(a > b\)); all the candies will be given to one of two sisters (i.e. \(a+b=n\)). Your task is to calculate the number of ways to distribute exactly \(n\) candies between sisters in a way described above. Candies are indistinguishable.Formally, find the number of ways to represent \(n\) as the sum of \(n=a+b\), where \(a\) and \(b\) are positive integers and \(a>b\).You have to answer \(t\) independent test cases.
The first line of the input contains one integer \(t\) (\(1 \le t \le 10^4\)) — the number of test cases. Then \(t\) test cases follow.The only line of a test case contains one integer \(n\) (\(1 \le n \le 2 \cdot 10^9\)) — the number of candies you have.
For each test case, print the answer — the number of ways to distribute exactly \(n\) candies between two sisters in a way described in the problem statement. If there is no way to satisfy all the conditions, print \(0\).
For the test case of the example, the \(3\) possible ways to distribute candies are: \(a=6\), \(b=1\); \(a=5\), \(b=2\); \(a=4\), \(b=3\).