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: Accepted)

#include<bits/stdc++.h>
#define mod 1000000007
using namespace std;
int n,f[1000005];
int sum;

int main(){
	cin>>n;
	f[0]=f[1]=1;
	sum=2;
	for(int i=2;i<=n;i++){
		f[i]=(sum-f[i-2]+mod)%mod;
		sum=(sum+f[i])%mod;
	}
	f[n]=(f[n]+1ll*f[n-1]*(n-1)%mod)%mod;
	for(int i=2;i<=n;i++) f[n]=(f[n]+1ll*(n-i+1)*f[n-i]%mod)%mod;
	int ans=f[n];
	for(int i=0;i<n-1;i++) ans=(ans+1ll*(n-1)*(n-1)%mod*f[i]%mod)%mod;
	cout<<ans<<endl;

	return 0;
}