A13450. Candies and Two Sisters

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:

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