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;
typedef long long ll;
ll n,dp[1000005],mod=1e9+7,sum,ans;
int main(){
    ios_base:: sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL);
    cin>>n;
    dp[n]=sum=n;
    for(ll i=n-1;i>0;i--){
      dp[i]=sum - dp[i+2] + ( (n-1)*(n-1))%mod + mod;
      dp[i]%=mod;
      dp[i]+=min(n-1,i+1);
      dp[i]%=mod;
      sum+=dp[i];
    }
    cout<<dp[1];
}