Interesting Array

You are given an array of $N$ elements. You are required to find the interval that is the most interesting.

We measure the value of interest of an interval as the product between $A$ and $B$, where $A$ is the frequency of the rarest element in the interval and $B$ is the frequency of the most common element. So, for the array $\{1, 3, 2, 3, 1, 2, 3\}$ we choose $A = 2$ and $B = 3$ for the interval $[1, 7]$.

Input

The first line of the input will contain the integer $N$ ($1 \leq N \leq 100\ 000$).
The second line of the input will contain $N$ integers separated by space representing the values of the array (the values will be between $1$ and $N$).

For $20\%$ of the points, $1 \leq N \leq 2\ 000$.

Output

The output will contain only one integer representing the highest value asked in the statement.

Example

stdin

5
1 2 1 3 2

stdout

2

Explanation

In the sample you may choose the intervals $[1, 3]$, $[1, 5]$ or $[2, 5]$; all of them have the rarest occurence of once ($2$ appears once in the interval $[1, 3]$) and the most common occurence of twice ($1$ appears twice in the interval $[1, 3]$).
Finally, $1 \cdot 2 = 2$.