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)

#pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
constexpr ll MODN = 1000000007;
ll n, dp[1000001];
int main() {
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	cin >> n, dp[0] = 1, dp[1] = dp[0] + n;
	for (int i = 2; i <= n; ++i) {
		dp[i] = (n - 1) * (n - 1);
		int l = i - (n + 1), r = i - 3;
		if (r >= 0) dp[i] += dp[r], r = -1;
		dp[i] += r - l + 1;
		dp[i] += 2 * dp[i - 1] - dp[i - 2];
		dp[i] %= MODN;
	}
	cout << (dp[n] - dp[n - 1] + MODN) % MODN << endl;
	return 0;
}