A11348. Vlad and Division

The first line contains a single integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases.

The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 2 \cdot 10^5$ ) — the total number of integers.

The second line of each test case contains $n$ given integers $a_1, \ldots, a_n$ ( $0 \leq a_j < 2^{31}$ ).

The sum of $n$ over all test cases in a test does not exceed $2 \cdot 10^5$ .

For each test case, output a single integer — the minimum number of groups required to satisfy the condition.

In the first test case, any two numbers have the same last $31$ bits, so we need to place each number in its own group.

In the second test case, $a_1=0000000000000000000000000000000_2$ , $a_2=1111111111111111111111111111111_2$ so they can be placed in the same group because $a_1(i) \ne a_2(i)$ for each $i$ between $1$ and $31$ , inclusive.

In the first test case, any two numbers have the same last $31$ bits, so we need to place each number in its own group.

In the second test case, $a_1=0000000000000000000000000000000_2$ , $a_2=1111111111111111111111111111111_2$ so they can be placed in the same group because $a_1(i) \ne a_2(i)$ for each $i$ between $1$ and $31$ , inclusive.