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>
int n,f[1000007],P=1000000007;
int main()
{
    scanf("%d",&n),f[n]=n,f[n-1]=1ll*n*n%P;
    for(int i=n-2,s=0;i>0;--i) (s+=f[i+3])%=P,f[i]=(f[i+1]+1ll*(n-1)*(n-1)+s+i+1)%P;
    printf("%d",f[1]);
}
