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;
using lint = long long;
using pi = pair<int, int>;
const int mod = 1e9 + 7;
const int MAXN = 2000005;

int n;
lint dp[MAXN], sum[MAXN];

int main(){
	cin >> n;
	for(int i=MAXN-1; i>=n; i--) dp[i] = 1, sum[i] = MAXN - i;
	for(int i=n-1; i>=0; i--){
		if(i <= n - 2){
		dp[i] = dp[i + 1] + 1ll * (n - 1) * (n - 1) % mod;
		dp[i] += sum[i + 3] - sum[i + n + 2] + mod;
		dp[i] %= mod;
		}
		else{
			dp[n - 1] = n;
		}
		sum[i] = (sum[i + 1] + dp[i]) % mod;
	}
	cout << dp[0] << endl;
}