A15093. Beat The Odds

Given a sequence $a_1, a_2, \ldots, a_n$ , find the minimum number of elements to remove from the sequence such that after the removal, the sum of every $2$ consecutive elements is even.

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 100$ ) — the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $3 \le n \le 10^5$ ).

The second line of each test case contains $n$ integers $a_1, a_2,\dots,a_n$ ( $1\leq a_i\leq10^9$ ) — elements of the sequence.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$ .

For each test case, print a single integer — the minimum number of elements to remove from the sequence such that the sum of every $2$ consecutive elements is even.

In the first test case, after removing $3$ , the sequence becomes $[2,4,6,8]$ . The pairs of consecutive elements are $\{[2, 4], [4, 6], [6, 8]\}$ . Each consecutive pair has an even sum now. Hence, we only need to remove $1$ element to satisfy the condition asked.

In the second test case, each consecutive pair already has an even sum so we need not remove any element.