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>
#include <cstring>
using namespace std;
typedef long long ll;
const int mod=1e9+7;
int n;
ll f[1000005];
int main(){
	scanf("%d",&n);
	f[1]=n;
	f[0]=1;
	ll sum=0;
	for(int i=2;i<=n;i++){
		f[i]=(sum+f[i-1]+1LL*(n-1)*(n-1)+(n-i+1))%mod;
		sum=(sum+f[i-2])%mod;
	}
	printf("%lld",f[n]);
	return 0;
}