1017C · The Phone Number

Problem: 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.

Input Format: The only line contains one integer $n$ ($1 \le n \le 10^5$) — the length of permutation that you need to build.

Output Format: Print a permutation that gives a minimum sum of lengths of LIS and LDS.

If there are multiple answers, print any.

Note: In the first sample, you can build a permutation $[3, 4, 1, 2]$. LIS is $[3, 4]$ (or $[1, 2]$), so the length of LIS is equal to $2$. LDS can be ony of $[3, 1]$, $[4, 2]$, $[3, 2]$, or $[4, 1]$. The length of LDS is also equal to $2$. The sum is equal to $4$. Note that $[3, 4, 1, 2]$ is not the only permutation that is valid.

In the second sample, you can build a permutation $[2, 1]$. LIS is $[1]$ (or $[2]$), so the length of LIS is equal to $1$. LDS is $[2, 1]$, so the length of LDS is equal to $2$. The sum is equal to $3$. Note that permutation $[1, 2]$ is also valid.