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;

const long long MOD = 1e9 + 7;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long n;
  cin >> n;
  vector<long long> dp(n + 2, 0);
  dp[n] = n;
  if(n > 1)
  dp[n - 1] = (n * n) % MOD;
  if(n > 2)
  dp[n - 2] = ((2 * n - 1) * n) % MOD;
  for(long long i = n - 3, cur = n - 1; i >= 1; i--)
  {
    (cur += dp[i + 3] + MOD - 1) %= MOD;
    (dp[i] += (n - 1) * (n - 1)) %= MOD;
    (dp[i] += dp[i + 1]) %= MOD;
    (dp[i] += cur) %= MOD;
  }
  cout << dp[1] << endl;
  return 0;
}
