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>
#include <string>
#include <cmath>
#include <algorithm>

using namespace std;

long long mod=1000000007;

int main(){
	long long n;
	cin >> n;
	long long x[1000001]={};
	x[0]=1;
	x[1]=n;
	x[2]=n*n%mod;
	for(int i=3;i<=n;i++){
		x[i]=(2*(x[i-1]+mod)-x[i-2]+x[i-3]-1)%mod;
	}
	cout << x[n] << endl;
	return 0;
}