#P1661C. Water the Trees
Water the Trees
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.
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.
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.
Samples
3
3
1 2 4
5
4 4 3 5 5
7
2 5 4 8 3 7 4
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 $4$.