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;

const int mo=int(1e9+7);
int n,f[1000010],ans;

void work()
{
	scanf("%d",&n);
	f[0]=1,f[1]=1;
	for (int i=2,s=2; i<=n; i++)
		f[i]=(s+mo-f[i-2])%mo,s=(s+f[i])%mo;
	for (int i=0; i<=n-2; i++)  ans=(ans+(1LL*(n-1)*(n-1)+(i+1))%mo*f[i])%mo;
	ans=(ans+1LL*f[n-1]*(n-1)+f[n])%mo;
	printf("%d",ans);
}

int main()
{
	work();
	return 0;
}
