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

• $1 \leq n \leq 10^6$

Sample Input 1Copy

2

Sample Output 1Copy

4

The four sequences that satisfy the conditions are:

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

Sample Input 2Copy

654321

Sample Output 2Copy

968545283