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<bits/stdc++.h>
using namespace std;

const int ha=1e9+7;
int f[2000010],n;

void add(int &x,const int &y){x=(x+y>=ha)?(x+y-ha):(x+y);}
void dev(int &x,const int &y){x=(x-y<0)?(x-y+ha):(x-y);}

int main()
{
    scanf("%d",&n);
    int sum=n-1;f[n]=n;
    for(int i=n+1;i<=2*n;i++) f[i]=1;
    for(int i=n-1;i>=1;i--)
    {
        add(f[i],f[i+1]);
        f[i]=(f[i]+1ll*(n-1)*(n-1))%ha;
        add(f[i],sum);
        dev(sum,f[i+n+1]);
        add(sum,f[i+2]);
    }
    printf("%d\n",f[1]);
    return 0;
}