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>
#include<algorithm>
#include<cmath>
#define mod 1000000007
#define maxn 1000010
using namespace std;
typedef long long ll;
ll n;
ll f[maxn];
int main(){
    scanf("%lld",&n);
    f[0]=1;
    f[1]=n;
    f[2]=n*n;
    ll now=0;
    for(int i=3;i<=n;i++)
    {
        f[i]=f[i-1];
        f[i]=(f[i]+(n-1)*(n-1)%mod)%mod;
        f[i]=(f[i]+now)%mod;
        f[i]=(f[i]+(ll)(n-i+2))%mod;
        now=(now+f[i-2])%mod;
    }
    printf("%lld\n",f[n]);
    return 0;
}