Solve the programming task below in a Python markdown code block.
Given two positive integers a and b, we define f(a, b) = \text{lcm}(a, b) - \gcd(a, b), where \text{lcm} denotes the [lowest common multiple] and \gcd denotes the [greatest common divisor].

Chef has a positive integer N. He wonders, what is the maximum value of f(a, b) over all pairs (a, b) such that a and b are positive integers, and a + b = N?

------ Input Format ------ 

- The first line of input will contain an integer T — the number of test cases. The description of T test cases follows.
- The first line of each test case contains an integer N, as described in the problem statement. 

------ Output Format ------ 

For each test case, output the maximum value of f(a, b) that can be obtained while satisfying the conditions on a and b. 

------ Constraints ------ 

$1 ≤ T ≤ 10^{5}$
$2 ≤ N ≤ 10^{9}$

----- Sample Input 1 ------ 
3
3
4
6

----- Sample Output 1 ------ 
1
2
4

----- explanation 1 ------ 
Test case $1$: There are two possible pairs of $(a, b)$: $(1, 2)$ and $(2, 1)$. For both of these pairs, we have $\text{lcm}(a, b) = 2$ and $\gcd(a, b) = 1$, which gives $f(a, b) = 1$. 

Test case $2$: For $(1, 3)$, we have $\text{lcm}(1, 3) = 3$ and $\gcd(1, 3) = 1$, giving $f(1, 3) = 3 - 1 = 2$. It can be shown that this is the maximum possible value of $f(a, b)$ that can be obtained while satisfying the above conditions. 

Test case $3$: For $(1, 5)$, we have $\text{lcm}(1, 5) = 5$ and $\gcd(1, 5) = 1$, giving $f(1, 5) = 5 - 1 = 4$. It can be shown that this is the maximum possible value of $f(a, b)$ that can be obtained while satisfying the above conditions.