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<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll N=1000000+10,P=1000000007;
ll f[N*2];
int main(){
	ll n,sum=0,ans=0;
	cin>>n;
    f[1]=1;
	for(ll i=1;i<=n;i++){
        f[i]=(f[i]+f[i-1])%P;
        if(i>=3) f[i]=((f[i]+sum-f[i-1]-f[i-2])%P+P)%P;
		if(i<n) ans=(ans+f[i]*(n-1)%P*(n-1)%P)%P;
		if(i<n-1) ans=(ans+f[i]*(i+1)%P)%P;
		else ans=(ans+f[i]*i%P)%P;
		sum=(sum+f[i])%P;
    }
	cout<<ans<<endl;
}