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>
#define N 1000000
#define MOD 1000000007
using namespace std;
typedef long long LL;
LL f[N+1];
LL solve()
{
	LL n; cin >> n;

	f[0] = 1;
	f[1] = n;
	f[2] = (n*n)%MOD;
	
	LL running_sum = (n*n+n+1)%MOD;
	for(LL k = 3; k <= n; k++)
	{
		f[k] = (running_sum-f[k-2]+(n*n-n-k+2))%MOD;
		running_sum += f[k], running_sum %= MOD;
	}
	return (f[n]+MOD)%MOD;
}
int main()
{
	cout<<solve()<<endl;
	return 0;
}