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>
typedef long long ll;

int n,f[1000005];
const int p=1000000007;

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