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
//AtCoder-2396
#include<cstdio>
#define ll long long
const int N=1e6+2,MOD=1e9+7;
int n,f[N],sum[N];
int main()
{
	f[1]=f[2]=f[0]=sum[0]=1;sum[1]=2;sum[2]=3;
	scanf("%d",&n);
	for(int i=3;i<=n;i++)
	{
		f[i]=f[i-1]+sum[i-3];
		f[i]-=f[i]>=MOD?MOD:0;
		sum[i]=sum[i-1]+f[i];
		sum[i]-=sum[i]>=MOD?MOD:0;
	}
	int ans=f[n];
	ans+=(ll)f[n-1]*(n-1)%MOD;
	ans-=ans>=MOD?MOD:0;
	for(int i=0;i<=n-2;i++)
	{
		ans+=(ll)f[i]*((ll)(n-1)*(n-1)%MOD+i+1)%MOD;
		ans-=ans>=MOD?MOD:0;
	}
	printf("%d",ans);
	return 0;
}