Problem Statement

You are given a positive integer $N$. Print an integer sequence of length $L \coloneqq N(N+1)/2$, $A = (A_1, A_2, \ldots, A_L)$, that satisfies all of the following conditions.

• $A$ contains exactly $i$ occurrences of $i$ for every $i = 1, 2, \ldots, N$.
• $1 \leq |A_i - A_{i+1}| \leq 2$ for every $i = 1, 2, \ldots, L$. Here, $A_{L+1}$ means $A_1$.

It can be proved that, under the Constraints of this problem, there is always an integer sequence $A$ of length $L$ that satisfies all of the above conditions.

Constraints

• $3 \leq N \leq 1000$
• $N$ is an integer.

Input

The input is given from Standard Input in the following format:

N

Output

Print the elements of $A$, separated by spaces, in the following format:

A_1 A_2 \ldots A_L

If multiple integer sequences $A$ of length $L$ satisfy the conditions in the problem statement, any one of them is accepted.