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: Wrong Answer)

#include<iostream>
#include<vector>

#define ll long long
using namespace std;
ll mod = 1e9 + 7;

int main()
{
	ll limit; cin >> limit;
	vector<ll>dp(limit);
	vector<ll>sum(limit);

	dp[0]=limit;
	for(int i=1;i<limit;i++){
		if(i>1)dp[i]=sum[i-2];
		if(i>2)dp[i]-=dp[i-3];
		dp[i]=(dp[i]+mod)%mod;
		dp[i]+=limit-i+2; dp[i]%=mod;
		dp[i]+=(limit-1)*(limit-1); dp[i]%=mod;
		sum[i]=sum[i-1]+dp[i]; sum[i]%=mod;
	}

	cout << dp[limit - 1] << endl;
	return 0;
}