Candies and Two Sisters

### 题面翻译 给你 $n$ 个糖果，你需要分给 Alice 和 Betty,求有多少种分法。 设 Alice 分到 $a$ 个，Betty 分到 $b$ 个，则分糖果的规则为： 1. Alice 和 Betty 的糖果都必须大于 $0$ $(a>0,b>0)$ 2. Alice 和 Betty 的糖果数均为整数 3. Alice 得到的糖果要比 Betty 多 $(a>b)$ 4. 所有的糖果都要分完 $(a+b=n)$ ### 输入格式 #### 本题有多组测试数据 第一行为一个整数 $t$，代表测试组数。 接下来 $t$ 行，对于每组测试数据，一行一个整数 $n$ 表示糖果的数目。 ### 输出格式 对于每组测试数据，一行一个整数表示有几种分法。 ### 说明/提示 $7$ 个糖果的分糖果方法为： - $a = 6, b = 1$ - $a = 5, b = 2$ - $a = 4, b = 3$ 共有 $3$ 种方法。

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 $ .

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