CF1556B.Take Your Places!

William has an array of $n$ integers $a_1, a_2, \dots, a_n$. In one move he can swap two neighboring items. Two items $a_i$ and $a_j$ are considered neighboring if the condition $|i - j| = 1$ is satisfied.

William wants you to calculate the minimal number of swaps he would need to perform to make it so that the array does not contain two neighboring items with the same parity.

威廉有一个由 $n$ 个整数组成的数组 $a_1, a_2, \dots, a_n$。在一次操作中，他可以交换两个相邻的元素。当且仅当 $|i - j| = 1$ 时，元素 $a_i$ 和 $a_j$ 被视为相邻。

威廉希望你计算出：为使数组中不存在两个相邻元素具有相同奇偶性（即同为奇数或同为偶数），他至少需要执行多少次交换操作。

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). Description of the test cases follows.

The first line of each test case contains an integer $n$ $(1 \le n \le 10^5)$ which is the total number of items in William's array.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ $(1 \le a_i \le 10^9)$ which are William's array.

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

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^4$）。随后是测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 10^5$），表示威廉数组中元素的总数。

第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le 10^9$），即威廉的数组。

保证所有测试用例的 $n$ 之和不超过 $10^5$。

For each test case output the minimal number of operations needed or $-1$ if it is impossible to get the array to a state when no neighboring numbers have the same parity.

对于每个测试用例，输出所需的最少操作次数；如果无法使数组满足“任意相邻两个数的奇偶性均不同”的状态，则输出 $-1$。

In the first test case the following sequence of operations would satisfy the requirements:

1. swap(2, 3). Array after performing the operation: $[6, 1, 6]$

In the second test case the array initially does not contain two neighboring items of the same parity.

In the third test case the following sequence of operations would satisfy the requirements:

1. swap(3, 4). Array after performing the operation: $[1, 1, 2, 1, 2, 2]$
2. swap(2, 3). Array after performing the operation: $[1, 2, 1, 1, 2, 2]$
3. swap(4, 5). Array after performing the operation: $[1, 2, 1, 2, 1, 2]$

In the fourth test case it is impossible to satisfy the requirements.

In the fifth test case the following sequence of operations would satisfy the requirements:

1. swap(2, 3). Array after performing the operation: $[6, 3, 2, 4, 5, 1]$
2. swap(4, 5). Array after performing the operation: $[6, 3, 2, 5, 4, 1]$

在第一个测试用例中，以下操作序列可满足要求：

1. swap(2, 3)。执行该操作后的数组：$[6, 1, 6]$

在第二个测试用例中，初始数组中不存在两个相邻的同奇偶性元素。

在第三个测试用例中，以下操作序列可满足要求：

1. swap(3, 4)。执行该操作后的数组：$[1, 1, 2, 1, 2, 2]$
2. swap(2, 3)。执行该操作后的数组：$[1, 2, 1, 1, 2, 2]$
3. swap(4, 5)。执行该操作后的数组：$[1, 2, 1, 2, 1, 2]$

在第四个测试用例中，无法满足要求。

在第五个测试用例中，以下操作序列可满足要求：

1. swap(2, 3)。执行该操作后的数组：$[6, 3, 2, 4, 5, 1]$
2. swap(4, 5)。执行该操作后的数组：$[6, 3, 2, 5, 4, 1]$