[Solution] The two numbers CodeChef Solution | CodeChef Problem Solution 2022

[Solution] The two numbers CodeChef Solution | CodeChef Problem Solution 2022

Given two positive integers a$a$ and b$b$, we define f(a,b)=lcm(a,b)−gcd(a,b)$f(a,b)=\text{lcm}(a,b)-gcd(a,b)$, where lcm$\text{lcm}$ denotes the lowest common multiple and gcd$gcd$ denotes the greatest common divisor.

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

Input Format

• The first line of input will contain an integer T$T$ — the number of test cases. 

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• The description of T$T$ test cases follows.
• The first line of each test case contains an integer N$N$, as described in the problem statement.

Output Format

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

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Constraints

• 1≤T≤105$1\le T\le {10}^5$
• 2≤N≤109