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 ll long long
using namespace std;
const int maxn=1000005;
const ll mod=1e9+7;
ll m,ans=0,f[maxn],s[maxn];
int n;
int main(){
	scanf("%d",&n);
	m=1ll*(n-1)*(n-1)%mod;
	ans=m+1+(n>2);
	f[0]=s[0]=1;
	for(int i=1;i<n;i++){
		f[i]=f[i-1]+(i>2?s[i-3]:0);
		s[i]=s[i-1]+f[i];
		f[i]%=mod;
		s[i]%=mod;
		if(i!=n-1)ans=(ans+1ll*f[i]*(m+min(n-1,i+2))%mod)%mod;
		else ans=(ans+1ll*f[i]*n%mod)%mod;
	}
	printf("%lld\n",ans);
	return 0;
}