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>
#define mp make_pair
#define pb push_back
#define pii pair<int,int>
#define LL long long
#define st first
#define nd second
#define endl '\n'
using namespace std;
LL n,dp[1000006],tt,mod=1e9+7;
int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cin>>n;
	dp[n]=n;
	tt=n;
	for(int i=n-1;i>=1;--i) {
		LL add;
		add=n-(n-i)+1;
		if(add==n) --add;
		dp[i]=((n-1)*(n-1)+tt+add+mod-dp[i+2])%mod;
		tt=(tt+dp[i])%mod;
	}
	cout<<dp[1]<<endl;
}