You are given an array $$$a$$$ of length $$$n$$$.

For any subarray, define its mode frequency as the maximum number of occurrences of any value within this subarray.

Find the maximum value of

over all subarrays.

Constraints: $$$1 \le n \le 2 \cdot 10^5$$$, $$$1 \le a_i \le n$$$.

Print the maximum possible value of the expression. Your answer will be accepted if its absolute or relative error does not exceed $$$10^{-6}$$$.

Give this interesting problem a try!