#P1370A. Maximum GCD
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ID: 5429
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Maximum GCD
No submission language available for this problem.
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 $b$.
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 $1 \leq a < b \leq n$.
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 $1 \leq a < b \leq n$.
Samples
2
3
5
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 $\mathrm{gcd}(2, 4)$.