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;

const ll MOD = 1e9 + 7;
const int N = 1e6 + 7;

ll n, f[N];

int main() {
  scanf("%lld", &n);
  f[0] = 1;
  f[1] = n;
  f[2] = (ll)n * n % MOD;
  ll cry = f[0] + n - 1;
  for(int i = 3; i <= n; i++) {
    f[i] = (f[i] + f[i - 1]) % MOD;
    f[i] = (f[i] + cry) % MOD;
    f[i] = ((n - i + 1) * (n) % MOD + f[i]) % MOD;
    cry = ((cry + n - 1) + f[i - 2]) % MOD;
  }
  printf("%lld\n", f[n]);
  return 0;
}
