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 int N = 1e6 + 7;
const int MOD = 1e9 + 7;

int dp[N];
int ps[N+1];

int main()
{
	ios::sync_with_stdio(false);

	dp[0] = 1;
	ps[1] = 1;
	for (int i=1; i<N; i++)
	{
		dp[i] = (dp[i-1] + ps[max(0, i-2)]) % MOD;
		ps[i+1] = (ps[i] + dp[i]) % MOD;
	}
	int n;
	cin >> n;
	ll res = n;
	for (int i=1; i<n; i++)
	{
		res = (res + 1LL * dp[i-1] * (n-1) % MOD * (n-1)) % MOD;
		res = (res + 1LL * dp[i] * (n-1)) % MOD;
	}
	cout << res << "\n";


	return 0;
}