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.

Examples

Input

2


Output

4


Input

654321


Output

968545283
#include <iostream>
#include <vector>

using namespace std;

const int MOD = 1000000007;

int main(){
	long long n;
	while(cin >> n){
		vector<long long> v(n+1, 1);
		vector<long long> s(n+1, 1);
		long long res = 0;
		for(int i=0;i<n;i++){
			if(i==n-1){
				res += (v[i] * n)%MOD;
			} else {
				long long sq = ((n-1) * (n-1)) % MOD;
				res += (v[i] * (sq + min(i+2LL, n-1))) %MOD;
			}
			res %= MOD;
			v[i+1] = s[i];
			if(i-1 >= 0) v[i+1] += (MOD - v[i-1]);
			v[i+1] %= MOD;
			s[i+1] = (s[i] + v[i+1])%MOD;
		}
		cout << res << endl;
	}
}

