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;
#define re register
#define in inline
#define ll long long
#define get getchar()
#define mian main
const int _=1e6+10;
const int mod=1e9+7;
ll f[_];
int main()
{
	ll n;
	scanf("%lld",&n);
	f[n]=n;
	f[n-1]=(n*n)%mod;
	ll ans=0;
	for (re int i=n-2; i>=1; i--)
	{
		ans=(ans+f[i+3])%mod;
		f[i]=((((f[i+1]+((n-1)*(n-1))%mod)%mod)+ans)%mod+i+1)%mod;
	}
	cout<<f[1]<<endl;
	return 0;
}
