Min Or Sum
Description
You are given an array $a$ of size $n$.
You can perform the following operation on the array:
- Choose two different integers $i, j$ $(1 \leq i < j \leq n$), replace $a_i$ with $x$ and $a_j$ with $y$. In order not to break the array, $a_i | a_j = x | y$ must be held, where $|$ denotes the bitwise OR operation. Notice that $x$ and $y$ are non-negative integers.
Please output the minimum sum of the array you can get after using the operation above any number of times.
Each test contains multiple test cases. The first line contains the number of test cases $t$ $(1 \leq t \leq 1000)$. Description of the test cases follows.
The first line of each test case contains an integer $n$ $(2 \leq n \leq 100)$ — the size of array $a$.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots ,a_n$ $(0 \leq a_i < 2^{30})$.
For each test case, print one number in a line — the minimum possible sum of the array.
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ $(1 \leq t \leq 1000)$. Description of the test cases follows.
The first line of each test case contains an integer $n$ $(2 \leq n \leq 100)$ — the size of array $a$.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots ,a_n$ $(0 \leq a_i < 2^{30})$.
Output
For each test case, print one number in a line — the minimum possible sum of the array.
Samples
4
3
1 3 2
5
1 2 4 8 16
2
6 6
3
3 5 6
3
31
6
7
Note
In the first example, you can perform the following operations to obtain the array $[1, 0, 2]$:
1. choose $i = 1, j = 2$, change $a_1 = 1$ and $a_2 = 2$, it's valid since $1 | 3 = 1 | 2$. The array becomes $[1, 2, 2]$.
2. choose $i = 2, j = 3$, change $a_2 = 0$ and $a_3 = 2$, it's valid since $2 | 2 = 0 | 2$. The array becomes $[1, 0, 2]$.
We can prove that the minimum sum is $1 + 0 + 2 = 3$
In the second example, We don't need any operations.