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 <algorithm>

using namespace std;

#define ll long long

ll f[1000001], p[1000001];
ll n;

const ll mod = 1000000007;

int main ()
{
  ios_base::sync_with_stdio (0);
  cin >> n;
  for (int i=1; i <= n; ++ i) f[i] = p[i] = 0;
  f[1] = p[1] = n;
  f[2] = n*n%mod;
  p[2] = (p[1] + f[2]) % mod;
  for (int i = 3; i <= n; i++)
    {
      f[i] = f[i - 1];
      f[i] += (n-1) * (n-1);
      f[i] += p[i-3];
      f[i] += n-i+2;
      f[i] %= mod;
      p[i] = (f[i] + p[i - 1]) % mod;
    }
  cout << f[n];
  return 0;
}
