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 ll long long
#define mod 1000000007
#define MN 1000000
ll f[MN+5],n;
int main(){
    ll sum=0;
    scanf("%d",&n);
    f[1]=n; f[2]=(n*n)%mod;
    for(int i=3;i<=n;i++){
        sum=(sum+f[i-3])%mod;
        f[i]=(sum+f[i-1]+(n-1)*(n-1)%mod+n-i+2)%mod;
    }
    cout<<f[n]; 
    return 0;  
}