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 <cstdio>

const int N = 1000000 + 10, MOD = 1000000007;

int n, f[N], g[N];

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