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>
const int md=1e9+7;
int n,ans,f[1000005],g[1000005];
int main(){
	scanf("%d",&n);
	ans=(n-1LL)*(n-1LL)%md;
	ans+=(n>2)+1;
	f[0]=g[0]=1;
	for(int i=1;i<n;++i){
		f[i]=(f[i-1]+((i>=3)?g[i-3]:0))%md,g[i]=(g[i-1]+f[i])%md;
		if(i<n-1)ans=(ans+((n-1LL)*(n-1)+i+1+(i!=n-2))%md*f[i])%md;else
		ans=(ans+1ll*n*f[i])%md;
	}
	printf("%d",ans);
	return 0;
}