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>  
using namespace std;      
typedef long long LL;  
const LL mod = 1e9+7;  
LL dp[1000003];  
int main()  
{  
    LL n,sum=0;  
    scanf("%lld",&n);  
    dp[1]=n;  
    dp[2]=(n*n)%mod;  
    for(int i=3;i<=n;++i)  
    {  
        sum=(sum+dp[i-3])%mod;  
        dp[i]=(dp[i-1]+sum+(n-1)*(n-1)%mod+n-i+2)%mod;  
    }  
    printf("%lld\n",dp[n]);  
    return 0;  
}  