#353 Permutation of the Year 1

Statement

Statement language

Let $N = 2026$ . A permutation $(a_1,a_2,\cdots,a_N)$ of $(1, 2, \cdots, N)$ is called a permutation of the year if it satisfies the following condition.

For every pair of integers $i,j$ ( $1 \leq i < j \leq N$ ), $(i-j)^2+(a_i-a_j)^2$ is divisible by .

Construct a permutation of the year.

Input

The input is given in the following format.

$N$

Output

Print a permutation of the year $a_1,a_2,\cdots,a_N$ on the first line, separated by spaces.

Constraints

$N=2026$ .

Subtasks

#	Score	Constraints
1	100	No additional constraints.

Samples

Input

13

Output

1 6 11 3 8 13 5 10 2 7 12 4 9

This sample is for reference only and is not included in the actual judge data.