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 int N = 1000010, MOD = 1e9 + 7;
typedef long long ll;
ll dp[N],sum;
int n;
int main() {
  scanf("%d",&n);
  dp[0] = 1;
  dp[1] = n;
  sum = 2 * n;
  for (int i = 2 ; i <= n ; ++ i) {
    dp[i] = 1ll * (n - 1) * (n - 1) % MOD;
    (dp[i] += sum - dp[i-2]) %= MOD;
    (sum += dp[i]) %= MOD;
    if (i - n >= 0) (sum -= dp[i-n]) %= MOD;
    else (sum -= 1) %= MOD;
  }
  printf("%lld\n",(dp[n] + MOD) % MOD);
  return 0;
}