Maximum Factors Problem solution codechef

You are given an integer $N$ . Let $K$ be a divisor of $N$ of your choice such that $K > 1$ , and let $M = \frac{N}{K}$ . You need to find the smallest $K$ such that $M$ has as many divisors as possible.

Note: $U$ is a divisor of $V$ if $V$ is divisible by $U$ .

Input Format

The first line of the input contains an integer $T$ – the number of test cases. The test cases then follow.
The only line of each test case contains an integer $N$ .

Output Format

For each test case, output in a single line minimum value of $K$ such that $M$ has as many divisors as possible.

Constraints

$1 \leq T \leq 3000$
$2 \leq N \leq 10^{9}$

Sample Input 1

Sample Output 1

3
2
2

Explanation

Test case $1$ : The only possible value for $K$ is $3$ , and that is the answer.
Test case $2$ : There are two cases:
- $K = 2$ . Then $M = \frac{4}{2} = 2$ , which has $2$ divisors ( $1$ and $2$ ).
- $K = 4$ . Then $M = \frac{4}{4} = 1$ , which has $1$ divisor ( $1$ ).

Therefore the answer is $2$ .

Test case $3$ : There are three cases:
- $K = 2$ . Then $M = \frac{6}{2} = 3$ , which has $2$ divisors ( $1$ and $3$ ).
- $K = 3$ . Then $M = \frac{6}{3} = 2$ , which has $2$ divisors ( $1$ and $2$ ).
- $K = 6$ . Then $M = \frac{6}{6} = 1$ , which has $1$ divisor ( $1$ ).

Therefore the answer is $2$ .

Maximum Factors Problem solution codechef

Maximum Factors Problem solution codechef

Input Format

Output Format

Constraints

Sample Input 1

Sample Output 1

Explanation

For Solution

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