A11884 | The Phone Number

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.