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;
int n;const int N=1e6+10;const int mod=1e9+7;
template<class T>inline void Inc(T&x,int y){x+=y;if(x>=mod) x-=mod;return;}
int f[N];
typedef long long ll;
int main()
{
	cin>>n;f[n]=n,f[n-1]=(ll)n*n%mod;int s=0;
	for(int i=n-2;i>0;--i) Inc(s,f[i+3]),f[i]=((ll)(n-1)*(n-1)%mod+f[i+1]+s+i+1)%mod;
	cout<<f[1]<<endl;
}
