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>
#include<algorithm>
#define MN 1000001
using namespace std;
 
const int MOD=1e9+7;
int n,f[MN],m;
inline void M(int &x){while(x>=MOD)x-=MOD;}
int main(){
    int i,j;
    scanf("%d",&n);f[n]=n;m=n-1;
    for (i=n-1;i;i--) f[i]=1LL*(n-1)*(n-1)%MOD,M(f[i]+=f[i+1]),M(f[i]+=m),M(m+=(i+2>n?1:f[i+2])-1);
    printf("%d\n",f[1]);
}