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>
#define MOD 1000000007
#define f(i,n) for(long long i=0;i<(long long)(n);i++)


int main(){
long long a,b,c,x,n;
scanf("%lld",&n);
a=1;
b=n;
c=n*n;
c=c%MOD;
if(n==1){
printf("1\n");
return 0;
}
f(i,n-2){
x=(2*c)-b+a-1;
x=(x+MOD)%MOD;
a=b;
b=c;
c=x;
}
printf("%lld\n",c);
return 0;
}