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<iostream>
#include<cstdio>
using namespace std;
#define inf 1000000007
int m,f[1000003],a;
int main()
{
    scanf("%d",&m);f[m]=m;
    f[m-1]=(long long)m*m%inf;
    for(int i=m-2;i>=1;--i)
    {
        a=(a+f[i+3])%inf;f[i]=f[i+1];
        f[i]=(f[i]+(long long)(m-1)*(m-1)%inf)%inf;
        f[i]=(f[i]+a)%inf;f[i]=(f[i]+i+1)%inf;
    }
    printf("%d\n",f[1]);
    return 0;
}