Mrs. Smith is trying to contact her husband, John Smith, but she forgot the secret phone number!

The only thing Mrs. Smith remembered was that any permutation of $$$n$$$ can be a secret phone number. Only those permutations that minimize secret value might be the phone of her husband.

The sequence of $$$n$$$ integers is called a permutation if it contains all integers from $$$1$$$ to $$$n$$$ exactly once.

The secret value of a phone number is defined as the sum of the length of the longest increasing subsequence (LIS) and length of the longest decreasing subsequence (LDS).

A subsequence $$$a_{i_1}, a_{i_2}, \ldots, a_{i_k}$$$ where $$$1\leq i_1 < i_2 < \ldots < i_k\leq n$$$ is called increasing if $$$a_{i_1} < a_{i_2} < a_{i_3} < \ldots < a_{i_k}$$$. If $$$a_{i_1} > a_{i_2} > a_{i_3} > \ldots > a_{i_k}$$$, a subsequence is called decreasing. An increasing/decreasing subsequence is called longest if it has maximum length among all increasing/decreasing subsequences.

For example, if there is a permutation $$$[6, 4, 1, 7, 2, 3, 5]$$$, LIS of this permutation will be $$$[1, 2, 3, 5]$$$, so the length of LIS is equal to $$$4$$$. LDS can be $$$[6, 4, 1]$$$, $$$[6, 4, 2]$$$, or $$$[6, 4, 3]$$$, so the length of LDS is $$$3$$$.

Note, the lengths of LIS and LDS can be different.

So please help Mrs. Smith to find a permutation that gives a minimum sum of lengths of LIS and LDS.