|Codeforces Round #634 (Div. 3)|
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:
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 $$$0$$$.
6 7 1 2 3 2000000000 763243547
3 0 0 1 999999999 381621773
For the test case of the example, the $$$3$$$ possible ways to distribute candies are: