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;
#define int long long
#define MOD 1000000007
int dp[1111111],su[1111111];

signed main(){
  int n;
  cin>>n;
  dp[0]=1;dp[1]=n;
  su[0]=1;su[1]=n+1;
  for(int i=2;i<=n;i++){
    dp[i]=(dp[i-1]+(i>=3?su[i-3]:0LL)+(n-1)*(n-1)+(n-i+1))%MOD;
    su[i]=(su[i-1]+dp[i])%MOD;
    //cout<<dp[i]<<endl;
  }
  cout<<dp[n]<<endl;
  return 0;
}
