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>
using namespace std;
#define MOD 1000000007
#define N 1000011
#define LL long long
LL n;
LL f[N],sum[N];
int main(){
	scanf("%lld",&n);
	f[0]=1;
	f[1]=n;f[2]=n*n%MOD;
	sum[1]=f[1]+1;sum[2]=(f[1]+f[2]+1)%MOD;sum[0]=f[0]=1;
	for(int i=3;i<=n;i++){
		f[i]=((f[i-1]+sum[i-3])%MOD+(n-1)*(n-1)%MOD+(n-i+1))%MOD;
		sum[i]=(sum[i-1]+f[i])%MOD;
	}
	printf("%lld\n",f[n]);
}
