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<cstdio>
#define ll long long
const int N=1e6+5,mo=1e9+7;
int n,i,s,f[N];
int main(){
	scanf("%d",&n);int v=(ll)(n-1)*(n-1)%mo;
	f[0]=1;f[1]=n;f[2]=(ll)n*n%mo;
	for (i=3;i<=n;i++) s=(s+f[i-3])%mo,
		f[i]=((ll)f[i-1]+s+v+(n-i+1))%mo;
	printf("%d",f[n]);
}