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<cstring>
using namespace std;
const long long Mod=1e9+7;
long long n,f[1000005],s[1000005],ans;
int main()
{
    scanf("%lld",&n);
    f[1]=f[2]=f[0]=s[0]=1;s[1]=2;s[2]=3;
    for(long long i=3;i<=n;i++)
    {
        f[i]=(f[i-1]+s[i-3])%Mod;
        s[i]=(s[i-1]+f[i])%Mod;
    }
    long long ans=f[n];
    ans=(ans+1ll*f[n-1]*(n-1)%Mod)%Mod;
    for(int i=0;i<=n-2;i++) ans=(ans+1ll*f[i]*(1ll*(n-1)*(n-1)%Mod+i+1)%Mod)%Mod;
    printf("%lld\n",1ll*ans);
    return 0;
}