Candies and Two Sisters

1000ms

262144K

Description:

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.

Input:

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.

Output:

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 $$$0$$$.

Sample Input:

Sample Output:

Note:

For the test case of the example, the $$$3$$$ possible ways to distribute candies are:

$$$a=6$$$, $$$b=1$$$;
$$$a=5$$$, $$$b=2$$$;
$$$a=4$$$, $$$b=3$$$.

Informação

Provedor Codeforces

Código CF1335A