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;
 
int main() {
  long n,ans=0,mod=1000000007,x=0,ziyu=1;
  cin >> n;
  vector<long> xx(n+100);
  for(long i=0;i<n-1;i++) {
    xx[i+2]=ziyu;
    ans=(ans+ziyu*min(n-1,i+2))%mod;
    ans=(ans+(ziyu*(n-1))%mod*(n-1))%mod;
    x=(x+xx[i])%mod;
    ziyu=(ziyu+x)%mod;
  }
  ans=(ans+(ziyu*n))%mod;
  cout << ans << endl;
}