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Contest: Task: Related: TaskC TaskE

Score : $1000$ points

Problem Statement

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 $10^9+7$.

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