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;
typedef long long ll;
const int N=1e6+100;
const int mod=1e9+7;
ll n;ll dp[N],m;
int main(){
    scanf("%lld",&n);
    dp[n]=n;m=n-1;
    for(int i=n-1;i;i--){
        dp[i]=(1ll*(n-1)*(n-1))%mod;
        dp[i]=(dp[i]+dp[i+1])%mod;
        dp[i]=(dp[i]+m)%mod;
        m+=((i+2>n?1:dp[i+2])-1)%mod;
    }
    printf("%lld\n",dp[1]%mod);
    //system("pause");
}