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.