#D3505. Candies and Two Sisters
Candies and Two Sisters
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.
inputFormat
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.
outputFormat
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.
样例
6
7
1
2
3
2000000000
763243547
3
0
0
1
999999999
381621773