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>
#define reg register
#define ll long long
#define inf 0x3f3f3f3f3f3f3f3f
using namespace std;
ll n,f[1000005],s;
int main()
{
    cin>>n;
    f[n]=n;
    f[n-1]=n*n%1000000007;
    for(reg int i=n-2;i>=1;i--)
    {
        s=(s+f[i+3])%1000000007;
        f[i]=(f[i+1]+(n-1)*(n-1)%1000000007+s+i+1)%1000000007;
    }
    printf("%d\n",f[1]);
}