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 int long long
#define mod 1000000007
using namespace std;
int n,f[1000005]={1},s[1000005]={1},ans=0;
signed main(){
	scanf("%lld",&n);
	if(n==1)return puts("1"),0;
	for(int i=1;i<n;i++){
		f[i]=f[i-1]+(i>=3?s[i-3]:0);
		s[i]=s[i-1]+f[i];
		f[i]%=mod;
		s[i]%=mod;
		//cout<<f[i]<<endl;
		if(i<n-1)ans+=((n-1)*(n-1)%mod+min(i+2,n-1))*f[i],ans%=mod;
	}
	printf("%lld\n",(ans+n*f[n-1]%mod+(n-1)*(n-1)+1+(n>2))%mod);
}