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>
#define ll long long
using namespace std;
const ll p=1e9+7;
ll n,i,sum,f[1000010];
int main(){
	scanf("%lld",&n);
	f[n]=n;f[n-1]=n*n%p;
	for(i=n-2;i>=1;i--){
		sum=(sum+f[i+3])%p;
		f[i]=(f[i+1]+(n-1)*(n-1)%p+sum+i+1)%p;
	}
	printf("%lld",f[1]);
}