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A. Candies and Two Sisters
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$0$$$.

Example
Input
6
7
1
2
3
2000000000
763243547
Output
3
0
0
1
999999999
381621773
Note

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

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