1335_A. 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.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The only line of a test case contains one integer n (1 ≤ n ≤ 2 ⋅ 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. 
```python
test = int(input())
for t in range(test):
    c = int(input())
    if c == 0 or c == 1 or c == 2:
        print(0)
    elif c % 2 == 0:
        print((c//2)-1)
    else:
        print(c//2)
```