Infinite Sequence

How many infinite sequences a_1, a_2, ... consisting of {{1, ... ,n}} satisfy the following conditions?

• The n-th and subsequent elements are all equal. That is, if n \leq i,j, a_i = a_j.
• For every integer i, the a_i elements immediately following the i-th element are all equal. That is, if i < j < k\leq i+a_i, a_j = a_k.

Find the count modulo 10^9+7.

Constraints

• 1 \leq n \leq 10^6

Input

Input is given from Standard Input in the following format:

n

Output

Print how many sequences satisfy the conditions, modulo 10^9+7.

Examples

Input

2

Output

4

Input

654321

Output

968545283

inputFormat

Input

Input is given from Standard Input in the following format:

n

outputFormat

Output

Print how many sequences satisfy the conditions, modulo 10^9+7.

Examples

Input

2

Output

4

Input

654321

Output

968545283

样例

654321

968545283