C. The Phone Number
constructive algorithms; greedy
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.
The only line contains one integer \(n\) (\(1 \le n \le 10^5\)) — the length of permutation that you need to build.
Print a permutation that gives a minimum sum of lengths of LIS and LDS. If there are multiple answers, print any.
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.