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$n$ candies. You want to distribute these n$n$ candies between two sisters in such a way that:

• Alice will get a$a$ (a>0$a>0$) candies;
• Betty will get b$b$ (b>0$b>0$) candies;
• each sister will get some integer number of candies;
• Alice will get a greater amount of candies than Betty (i.e. a>b$a>b$);
• all the candies will be given to one of two sisters (i.e. a+b=n$a+b=n$).

Your task is to calculate the number of ways to distribute exactly n$n$ candies between sisters in a way described above. Candies are indistinguishable.

Formally, find the number of ways to represent n$n$ as the sum of n=a+b$n=a+b$, where a$a$ and b$b$ are positive integers and a>b$a>b$.

You have to answer t$t$ independent test cases.

Input

The first line of the input contains one integer t$t$ (1≤t≤104$1\le t\le {10}^4$) — the number of test cases. Then t$t$ test cases follow.

The only line of a test case contains one integer n$n$ (1≤n≤2⋅109$1\le n\le 2\cdot {10}^9$) — the number of candies you have.

Output

For each test case, print the answer — the number of ways to distribute exactly n$n$ candies between two sisters in a way described in the problem statement. If there is no way to satisfy all the conditions, print 0$0$.

Example

input

Copy

6
7
1
2
3
2000000000
763243547

output

Copy

3
0
0
1
999999999
381621773

Note

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

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

Solution With C++

#include<bits/stdc++.h>

using namespace std;

void printCandis(int arr[],int t)

{

    for(int i=0;i<t;i++)

    {

        if(arr[i]==1||arr[i]==2)

        {

            cout<<"0"<<endl;

        }

        else

        {

            cout<<(arr[i]-1)/2<<endl;

        }

    }

}

int main()

{

   int t;

   cin>>t;

   int arr[t];

   for(int i=0;i<t;i++)

   {

       cin>>arr[i];

   }

   printCandis(arr,t);

}