A15060 | Water the Trees

There are $n$ trees in a park, numbered from $1$ to $n$ . The initial height of the $i$ -th tree is $h_i$ .

You want to water these trees, so they all grow to the same height.

The watering process goes as follows. You start watering trees at day $1$ . During the $j$ -th day you can:

- Choose a tree and water it. If the day is odd (e.g. $1, 3, 5, 7, \dots$ ), then the height of the tree increases by $1$ . If the day is even (e.g. $2, 4, 6, 8, \dots$ ), then the height of the tree increases by $2$ .
- Or skip a day without watering any tree.

Note that you can't water more than one tree in a day.

Your task is to determine the minimum number of days required to water the trees so they grow to the same height.

You have to answer $t$ independent test cases.

The first line of the input contains one integer $t$ ( $1 \le t \le 2 \cdot 10^4$ ) — the number of test cases.

The first line of the test case contains one integer $n$ ( $1 \le n \le 3 \cdot 10^5$ ) — the number of trees.

The second line of the test case contains $n$ integers $h_1, h_2, \ldots, h_n$ ( $1 \le h_i \le 10^9$ ), where $h_i$ is the height of the $i$ -th tree.

It is guaranteed that the sum of $n$ over all test cases does not exceed $3 \cdot 10^5$ ( $\sum n \le 3 \cdot 10^5$ ).

For each test case, print one integer — the minimum number of days required to water the trees, so they grow to the same height.