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>
#define LL long long
#define N 1000010
#define M 1000000007
LL n,f[N],sum;
int main()
{
	scanf("%lld",&n);
	f[n]=n,f[n-1]=(LL)n*n%M;
	for(LL i=n-2;i>=1;--i)
	{
		sum=(sum+f[i+3])%M;
		f[i]=f[i+1];
		f[i]=(f[i]+(LL)(n-1)*(n-1)%M)%M;
		f[i]=(f[i]+sum)%M;
		f[i]=(f[i]+i+1)%M;
	}
	printf("%lld\n",f[1]);
	return 0;
}