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>
const int MAXN=1e6+10,Mod=1e9+7;long long n,f[MAXN],s;int main(){scanf("%lld",&n);f[1]=n;f[2]=n*n%Mod;for(int i=3;i<=n;++i)f[i]=(((f[i-1]+s)%Mod+(n-1)*(n-1)%Mod)%Mod+(n-i+2))%Mod,(s+=f[i-2])%=Mod;printf("%lld\n",f[n]);return 0; }