The Struggling Contestant

一共有 $n$ 道题，题号从 $1$ 到 $n$，其中题号为 $i$ 的题有一个标签 $a_i$。 需要确定一个做完 $n$ 道题的顺序，使得所做的任意连续两道题的标签均不相同，且连续两道题之间题号不相邻的次数尽可能少，求出这个次数的最小值。 形式化地，对于一个长度为 $n$ 的排列 $p$，定义 $p$ 的花费为满足 $1\le i<n$ 且 $|p_{i+1}-p_i|>1$ 的下标 $i$ 的个数。现要求对于所有的 $1\le i<n$，有 $a_{p_i}\neq a_{p_{i+1}}$，输出满足条件的排列 $p$ 的最小花费。 若没有满足条件的排列，输出 $-1$。 有多组测试数据。

To help those contestants who struggle a lot in contests, the headquarters of Codeforces are planning to introduce Division 5. In this new division, the tags of all problems will be announced prior to the round to help the contestants. The contest consists of $ n $ problems, where the tag of the $ i $ -th problem is denoted by an integer $ a_i $ . You want to AK (solve all problems). To do that, you must solve the problems in some order. To make the contest funnier, you created extra limitations on yourself. You do not want to solve two problems consecutively with the same tag since it is boring. Also, you are afraid of big jumps in difficulties while solving them, so you want to minimize the number of times that you solve two problems consecutively that are not adjacent in the contest order. Formally, your solve order can be described by a permutation $ p $ of length $ n $ . The cost of a permutation is defined as the number of indices $ i $ ( $ 1\le i<n $ ) where $ |p_{i+1}-p_i|>1 $ . You have the requirement that $ a_{p_i}\ne a_{p_{i+1}} $ for all $ 1\le i< n $ . You want to know the minimum possible cost of permutation that satisfies the requirement. If no permutations meet this requirement, you should report about it.

The first line contains a single integer $ t $ ( $ 1\leq t\leq 10^4 $ ) — the number of test cases. The first line of the description of each test case contains a single integer $ n $ ( $ 1 \le n \le 10^5 $ ) — the number of problems in the contest. The next line contains $ n $ integers $ a_1,a_2,\ldots a_n $ ( $ 1 \le a_i \le n $ ) — the tags of the problems. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ .

For each test case, if there are no permutations that satisfy the required condition, print $ -1 $ . Otherwise, print the minimum possible cost of a permutation that satisfies the required condition.

4
6
2 1 2 3 1 1
5
1 1 1 2 2
8
7 7 2 7 7 1 8 7
10
1 2 3 4 1 1 2 3 4 1

1
3
-1
2

In the first test case, let $ p=[5, 4, 3, 2, 1, 6] $ . The cost is $ 1 $ because we jump from $ p_5=1 $ to $ p_6=6 $ , and $ |6-1|>1 $ . This permutation is valid because we don't solve problems with the same tag twice in a row. We cannot find a permutation with a cost smaller than $ 1 $ . In the second test case, let $ p=[1,5,2,4,3] $ . The cost is $ 3 $ because $ |p_2-p_1|>1 $ , $ |p_3-p_2|>1 $ , and $ |p_4-p_3|>1 $ . The permutation is valid because we don't solve problems with the same tag twice in a row. We cannot find a permutation with a cost smaller than $ 3 $ . In the third test case, for any order of solving the problems, we will solve two problems with the same tag consecutively, so the answer is $ -1 $ .