A13481. Maximum GCD

Let's consider all integers in the range from $1$ to $n$ (inclusive).

Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of $\mathrm{gcd}(a, b)$ , where $1 \leq a < b \leq n$ .

The greatest common divisor, $\mathrm{gcd}(a, b)$ , of two positive integers $a$ and $b$ is the biggest integer that is a divisor of both $a$ and $b$ .

The first line contains a single integer $t$ ( $1 \leq t \leq 100$ ) — the number of test cases. The description of the test cases follows.

The only line of each test case contains a single integer $n$ ( $2 \leq n \leq 10^6$ ).

For each test case, output the maximum value of $\mathrm{gcd}(a, b)$ among all $1 \leq a < b \leq n$ .

In the first test case, $\mathrm{gcd}(1, 2) = \mathrm{gcd}(2, 3) = \mathrm{gcd}(1, 3) = 1$ .

In the second test case, $2$ is the maximum possible value, corresponding to $\mathrm{gcd}(2, 4)$ .