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>
#include <cstring>
#include <algorithm>
#define MOD 1000000007

using namespace std;

typedef long long ll;

ll f[1000005];

int main() {
  int n;
  scanf("%d",&n);
  f[1]=n;
  ll s=n-1;
  for(int i=2;i<=n;i++) {
  	if (i>=4) s=(s+f[i-3]-1+MOD)%MOD;
  	f[i]=(f[i-1]+(ll)(n-1)*(n-1)+s)%MOD;
  }
  printf("%lld\n",f[n]);
  return 0;
}