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 <cstdio>
using namespace std;

typedef long long ll;

const int MOD = 1000000007;
int D[1000010];
ll S[1000010];

int main() {
  int n; scanf("%d", &n);
  D[0] = 1; D[1] = n;
  S[0] = 1; S[1] = n + 1;
  for(int i=2;i<=n;i++){
    D[i] = ((ll)(n-1) * (i-2) + (ll)(n - i + 1) * n + D[i-1] + (i>=3?S[i-3]:0)) % MOD;
    S[i] = (S[i-1] + D[i]) % MOD;
  }
  printf("%d\n", D[n]);
  return 0;
}
