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>
#define M 1000005
#define L long long
#define MOD 1000000007
using namespace std;
L f[M]={0},g[M]={0};
int main(){
	L n,ans=0; cin>>n;
	f[1]=1;
	for(L i=1;i<=n;i++){
		f[i]=(f[i]+(i>=3?g[i-3]:0)+f[i-1])%MOD;
		g[i]=(g[i-1]+f[i])%MOD;
		if(i<n) ans=(ans+f[i]*(n-1)%MOD*(n-1)+f[i]*min(n-1,i+1))%MOD;
	}
	ans=(ans+f[n]*n)%MOD;
	cout<<ans<<endl;
}