Equalize the Array

Source: HackerRank

Version: Phuoc Hung OJ Extended

Problem

Given an integer array of length $n$, delete the minimum number of elements so that all remaining elements are equal. Let

Keeping a value $v$ requires $n-f(v)$ deletions, hence the answer is

Compute $D$.

Input

The first line contains $n$. The second line contains $n$ integers $a_i$.

Output

Print $D$, the minimum number of deletions.

Subtask

Subtask 1 (20 points): $1\le n\le10$, $1\le a_i\le100$.

Subtask 2 (30 points): $1\le n\le50$, $1\le a_i\le100$.

Subtask 3 (50 points): $1\le n\le100$, $1\le a_i\le100$.

Example

Input

5
3 3 2 1 3

Output

2

Explanation

The output follows directly from the mathematical definition above.