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;
long long n,i,s=0,f[1000005];
int main(){
	cin>>n;
    f[n]=n;
    f[n-1]=n*n%1000000007;
    for(i=n-2;i>0;i--){
    s=(s+f[i+3])%1000000007;
    f[i]=f[i+1];
    f[i]=(f[i]+((n-1)*(n-1)%1000000007))%1000000007;
    f[i]=(f[i]+s)%1000000007;
    f[i]=(f[i]+i+1)%1000000007;
    }
    cout<<f[1]<<endl;
}