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;
#define MOD 1000000007
int n,f[1000010];
int main()
{
	scanf("%d",&n);f[n]=n;f[n-1]=1ll*n*n%MOD;
	for(int i=n-2,s=0;i>0;--i)s=(s+f[i+3])%MOD,f[i]=(f[i+1]+1ll*(n-1)*(n-1)+s+i+1)%MOD;
	printf("%d\n",f[1]);
	return 0;
}
