Problem:
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

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

n,s,d[2],m=1e9+7;main(i){for(scanf("%d",&n),d[0]=s=1;++i<n;s=(s+d[i&1])%m)d[i&1]=(m+s-d[i&1])%m;printf("%d\n",(1+s*n%m+m-d[1-n%2]*(n-1)%m)*(n-1)%m);}