Questionnaire

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 524288/524288 K (Java/Others)

Description

In order to get better results in official ACM/ICPC contests, the team leader comes up with a questionnaire. He asked everyone in the team whether to have more training.



Picture from Wikimedia Commons


Obviously many people don't want more training, so the clever leader didn't write down their words such as ''Yes'' or ''No''. Instead, he let everyone choose a positive integer $a_i$ to represent his opinion. When finished, the leader will choose a pair of positive interges $m(m>1)$ and $k(0\leq k<m)$, and regard those people whose number is exactly $k$ modulo $m$ as ''Yes'', while others as ''No''. If the number of ''Yes'' is not less than ''No'', the leader can have chance to offer more training.

Please help the team leader to find such pair of $m$ and $k$.

Input

The first line of the input contains an integer $T(1\leq T\leq15)$, denoting the number of test cases.

In each test case, there is an integer $n(3\leq n\leq 100000)$ in the first line, denoting the number of people in the ACM/ICPC team.

In the next line, there are $n$ distinct integers $a_1,a_2,...,a_n(1\leq a_i\leq 10^9)$, denoting the number that each person chosen.

Output

For each test case, print a single line containing two integers $m$ and $k$, if there are multiple solutions, print any of them.

Sample Input

1 6 23 3 18 8 13 9

Sample Output

5 3

Hint

liuyiding

Source

2017 Multi-University Training Contest - Te

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