Problem Description

tada72 found a strange paper. The paper said, "This paper contains $1$ twice, $2$ three times, $3$ twice, and $4$ once." Inspired by this, he wanted to create more papers with similar properties.

Given an integer $N$, determine if there exists a sequence $A$ of length $N$ that satisfies the following two conditions. If it exists, construct it.

• All elements of the sequence are integers between $1$ and $N$ inclusive.
• For all integers $i$ satisfying $1 \leq i \leq N$, there are exactly $A_i - 1$ integers $j$ such that $i = A_j$ (where $1 \leq j \leq N$).

Input Format

The input is given from the standard input in the following format:

$ N $

Output Format

If no sequence $A$ satisfies the conditions, output -1 in one line. If it exists, output the sequence $A$ in the following format:

$ A_1 $ $ A_2 $ $\ldots$ $ A_N $

Note that if multiple sequences $A$ satisfy the conditions, you may output any one of them.

Sample Input and Output

Sample Input #1

4

Sample Output #1

2 3 2 1

Sample Input #2

2

Sample Output #2

-1

Notes/Hints

Constraints

• $1 \leq N \leq 10^5$
• All inputs are integers.

Sample Explanation 1

$A$ contains $1$ once, $2$ twice, $3$ once, and $4$ zero times, satisfying the conditions.

Sample Explanation 2

Original idea: tada72

见题面 Input 部分

见题面 Output 部分