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
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
#include<iostream>
#include<cstdio>
#include<cstring>
#define ll long long
#define p 1000000007
using namespace std;
namespace ywy{
	ll f[1000001],sums[1000001];
	void ywymain(){
		int n;cin>>n;f[0]=1;f[1]=n;f[2]=((ll)n*(ll)n)%p;sums[0]=1;sums[1]=n+1;sums[2]=(f[2]+sums[1])%p;
		for(register int i=3;i<=n;i++){
			f[i]=(f[i-1]+sums[i-3]+n-i+1)%p;f[i]+=(ll)(n-1)*(ll)(n-1);f[i]%=p;sums[i]=(sums[i-1]+f[i])%p;
		}cout<<f[n]<<endl;
	}
}
int main(){
	ywy::ywymain();return(0);
}