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>

#define MAXN 1000010
#define mod 1000000007

unsigned long long n,f[MAXN],add;

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