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>
#define MN 1000005
using namespace std;
const int mod=1e9+7;
int dp[MN],sum[MN],n,res;
int main(){
	scanf("%d",&n);dp[0]=sum[0]=1;res=1ll*(n-1)*(n-1)%mod;
	for(int i=1;i<n;i++){
		dp[i]=dp[i-1]+(i-3>=0?sum[i-3]:0),dp[i]%=mod;
		sum[i]=sum[i-1]+dp[i],sum[i]%=mod;
		if(i<n-1)res+=1ll*dp[i]*(n-1)%mod*(n-1)%mod,res%=mod;else res+=1ll*dp[i]*(n-1)%mod,res%=mod;
	}
	for(int i=0;i<n-1;i++)dp[n]+=1ll*dp[i]*((i+n+1)-max(n,i+3)+1)%mod,dp[n]%=mod;res+=(dp[n]+dp[n-1])%mod;printf("%d\n",res%=mod);
}