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 <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 10;
const int Mod = 1000000007;
int n,m,f[N],ans;
int main()
{
	cin>>n;
	m=(1ll*(n-1)*(n-1))%Mod;
	if(n>2) ans=m+2;
	else ans=m+1;
	int sum=f[0]=1;
	for(int i=1;i<n;i++)
	{
		f[i]=sum;
		if(i-2>=0) f[i]=(f[i]-f[i-2]+Mod)%Mod;
		sum=(sum+f[i])%Mod;
		if(i!=n-1) ans=(ans+1ll*f[i]*(m+min(i+2,n-1))%Mod)%Mod;
        else ans=(ans+1ll*f[i]*n%Mod)%Mod;
	}
	cout<<ans<<"\n";
}