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++14 (GCC 5.4.1) (judge verdict: Accepted)

# include<iostream>
# include<cstring>
# include<cstdio>
# include<algorithm>
using namespace std;
const int MAX=1e6+5,mod=1e9+7;
int n;
int f[MAX];
int main()
{
	scanf("%d",&n),f[n]=n,f[n-1]=1ll*n*n%mod;
	for(int i=n-2,sum=0;i>=1;--i)
	  (sum+=f[i+3])%=mod,(f[i]+=((1ll*(n-1)*(n-1)%mod+f[i+1])%mod+i+1+sum)%mod)%=mod;
	return printf("%d",f[1]),0;
}