As part of your mandatory forty hours of community service, you have been tasked with getting rid of some rather unsightly icicles outside of Martingrove.

There are ~N~ icicles that you were tasked with destroying, with the ~i^\text{th}~ icicle having a length of ~L_i~. When you destroy an icicle its length is set to ~0~. After careful examination, you realize that the icicles can be spared for aesthetic reasons if they are symmetrical. That is, a sequence of ~N~ icicles is considered symmetrical if the ~i^\text{th}~ icicle from the left has the same length as the ~i^\text{th}~ icicle from the right.

What is the minimum number of icicles that you must destroy?

Constraints

~1 \le N, L_i \le 10^6~

Input Specification

The first line contains the integer ~N~.

The second line contains ~N~ integers, where the ~i^\text{th}~ integer represents the length of the ~i^\text{th}~ icicle.

Output Specification

Output a single integer, the minimum number of icicles needed to be destroyed.

Sample Input

5
3 2 1 4 3

Sample Output

2

Explanation for Sample

By destroying the ~2^\text{nd}~ and ~4^\text{th}~ icicles, the icicles are now symmetrical.