Even Odd GCD (Easy Version)

Even Odd GCD (Easy Version)

You cannot submit for this problem because the contest is ended. You can click "Open in Problem Set" to view this problem in normal mode.

Time Limit: 1.0 s

Memory Limit: 256.0 MB

Description

You are given an array \(A[]\) and the length of the array is N. You need to rearrange array \(A[]\) such way that sum of GCD odd index and even index is as maximum as possible.

Let's see,

  • Odd index GCD of array \(A[]\), X = GCD \((A_1, A_3, A_5,...A_N)\). ( all odd index between 1 to N)

  • Even index GCD of array \(A[]\), Y = GCD \((A_2, A_4, A_6,...A_N)\). ( all even index between 1 to N)

After rearrange of array \(A[]\), Find Maximum possible sum of X+Y.

GCD means Greatest Common Divisor. For example,

GCD(2,4,6) = 2, that means 2 is the largest possible number which divide all number appear in the set.

Note : Difference between easy and hard version is limit of N and array A[] elements.

Input

T : Number of test case.
N : Length of the array A[].
A[] : Exactly N elements.

\(1 <= T <= 100\)
\(2 <= N <= 100\)
\(1 <= A[] <= 100\)

Output

In each test case, print the maximum sum.

Sample

Input Output
2
5
12 27 21 14 15
2
2 5
10
7

First test case:

Bangladesh 2.0

Not Attended
Status
Done
Rule
ACM/ICPC
Problem
8
Start at
2024-08-16 15:30
End at
2024-08-16 17:45
Duration
2.2 hour(s)
Host
Partic.
133