Maximum GCD

1000ms

262144K

Description:

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 $$$b$$$.

Input:

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 $$$n$$$ ($$$2 \leq n \leq 10^6$$$).

Output:

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

Sample Input:

2
3
5

Sample Output:

1
2

Note:

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 $$$\mathrm{gcd}(2, 4)$$$.

Informação

Provedor Codeforces

Código CF1370A