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;

#define REP(i, n) for (int i = 0; i < (n); ++i)

const int N = 1000005;

const int mod = 1000*1000*1000+7;

int n;
int f[N], g[N];

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);

	cin >> n;

	int result = 0;

	f[0] = 1;

	for (int i = 1; i <= n; ++i) {
		g[i] = (g[i] + g[i - 1]) % mod;
		f[i] = (f[i] + f[i - 1]) % mod;
		f[i] = (f[i] + g[i]) % mod;
		if (i + 1 <= n) {
			result = (result + (1LL * (n - 1) * (n - 1) % mod) * f[i - 1]) % mod;
		}
		if (i + 2 <= n) {
			g[i + 2] = (g[i + 2] + f[i - 1]) % mod;
			result = (result + 1LL * f[i - 1] * i) % mod;
		} else {
			result = (result + 1LL * f[i - 1] * (n - 1)) % mod;
		}
		// for (int j = 2; j <= n; ++j) {
		// 	if (i + j <= n) {
		// 		f[i + j] = (f[i + j] + f[i]) % mod;
		// 	} else {
		// 		result = (result + f[i]) % mod;
		// 	}
		// }
	}

	result = (result + f[n]) % mod;

	cout << result << endl;

	return 0;
}