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>
long long n,f[1000001],sum;
int main()
{
	scanf("%lld",&n);
	f[1]=n;f[2]=n*n;
	for(int i=3;i<=n;++i){
		f[i]=(f[i-1]+(n-i+2)*f[1]+sum)%1000000007;
		sum=(sum+f[i-2]+n-1)%1000000007;
	}
	printf("%lld\n",f[n]);
	return 0;
}