Water the Trees

3000ms

262144K

Description:

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.

Input:

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 $$$3 \cdot 10^5$$$ ($$$\sum n \le 3 \cdot 10^5$$$).

Output:

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

Sample Input:

3
3
1 2 4
5
4 4 3 5 5
7
2 5 4 8 3 7 4

Sample Output:

4
3
16

Note:

Consider the first test case of the example. The initial state of the trees is $$$[1, 2, 4]$$$.

During the first day, let's water the first tree, so the sequence of heights becomes $$$[2, 2, 4]$$$;
during the second day, let's water the second tree, so the sequence of heights becomes $$$[2, 4, 4]$$$;
let's skip the third day;
during the fourth day, let's water the first tree, so the sequence of heights becomes $$$[4, 4, 4]$$$.

Thus, the answer is $$$4$$$.

Informação

Provedor Codeforces

Código CF1661C