CF1691A 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.