Minimize Multiples Of Three

One operation adds 1 to or subtracts 1 from a number. Find the minimum total number of operations needed to make every array element divisible by 3.

This site's standard input/output format and supplementary bounds follow this problem's description.

输入格式

The first line contains n (1≤n≤2×10^5), and the second line contains n integers (|a[i]|≤10^9).

输出格式

Output the minimum number of operations.

样例 1

输入：

4
12 21 3 4

输出：

1

样例 2

输入：

2
4 5

输出：

2

样例 3

输入：

3
-2 0 7

输出：

2