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 int long long
const int N=1000005,M=1e9+7;
int n,f[N],sum;
signed main(){
	scanf("%lld",&n);
	f[n]=sum=n;f[n+1]=1;
	for (int i=n-1;i;i--){
		(f[i]+=(n-1)*(n-1))%=M;
		(f[i]+=sum+i+1-f[i+2]+M)%=M;
		(sum+=f[i])%=M;
	}
	printf("%lld\n",f[1]);
}