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 pair<int,int> PII;
typedef long long ll;
const ll mod = 1e9+7;

ll dp[2000100];

int main(void){
  ll n;
  cin >> n;
  fill(dp,dp+2000100,1);
  dp[n] = n;
  ll sum = n-1;
  for(int i = n-1;i > 0;--i){
    dp[i] = dp[i+1];
    dp[i] += (n-1)*(n-1);
    dp[i] %= mod;
    dp[i] += sum;
    dp[i] %= mod;
    sum -= dp[i+1+n];
    sum = (sum+mod) % mod;
    sum += dp[i+2];
    sum %= mod;
  }
  cout << dp[1] << endl;
  return 0;
}
