
Score : 1000 points
Problem StatementHow 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
InputInput is given from Standard Input in the following format:
n
OutputPrint how many sequences satisfy the conditions, modulo 10^9+7.
Sample Input 12
Sample Output 14
The four sequences that satisfy the conditions are:
1, 1, 1, ...
1, 2, 2, ...
2, 1, 1, ...
2, 2, 2, ...
Sample Input 2654321
Sample Output 2968545283
