infiniteseq

Title

Problem Statement

How many infinite sequences a₁, a₂, ... consisting of {{1, ... ,n}} satisfy the following conditions?

• The n-th and subsequent elements are all equal. That is, if n ≤ 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≤ i+a_i, a_j = a_k.

Find the count modulo 10⁹+7.

Constraints

• 1 ≤ n ≤ 10⁶

Input

Input is given from Standard Input in the following format:

n

Output

Print how many sequences satisfy the conditions, modulo 10⁹+7.

Sample Input 1

2

Sample Output 1

4

The four sequences that satisfy the conditions are:

• 1, 1, 1, ...
• 1, 2, 2, ...
• 2, 1, 1, ...
• 2, 2, 2, ...

Sample Input 2

654321

Sample Output 2

968545283