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

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