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>
const int mo=1000000007;
int sum[1000005];
int main(){
	int n,ans;
	scanf("%d",&n);
	ans=1ll*n*n%mo;
	sum[1]=n;sum[2]=(ans+n)%mo;
	for (int i=3;i<=n;i++){
		ans=(ans+sum[i-3]+1ll*n*(n-1)-i+3)%mo;
		sum[i]=(sum[i-1]+ans)%mo;
	}
	printf("%d\n",ans);
}