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>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=1e6+7,mod=1000000007;
int n,m,ans,f[N],s[N];
int main()
{
	scanf("%d",&n);
	f[1]=1;
	for(int i=1;i<=n;i++)
	{
		if(i>=3)f[i]=(f[i]+s[i-3])%mod;
		f[i]=(f[i]+f[i-1])%mod;
		s[i]=(s[i-1]+f[i])%mod;
	}
	ans=1ll*f[n]*n%mod;
	for(int i=1;i<n;i++)ans=(ans+1ll*f[i]*(n-1)%mod*(n-1)+1ll*f[i]*min(i+1,n-1))%mod;
	printf("%d\n",ans);
}