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>
using namespace std;
typedef long long ll;
const int N=1001000,P=1000000007;
int i,j,k,n,m,sum;
int f[N];
int main() {
	scanf("%d",&n);
	f[1]=n;f[2]=(ll) n*n%P;sum=((ll) n*n+n)%P;
	for (i=3;i<=n;i++) {
		f[i]=((ll) (n-1)*(n-1)+(n-i+2)+sum+P-f[i-2])%P;
		sum=(sum+f[i])%P;
	}
	printf("%d\n",f[n]);
}