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;
#define P 1000000007
long long ans,sum,f[1000005],g[1000005];int n;
int main()
{
    scanf("%d",&n);f[1]=1;
    for(int i=1;i<=n;i++) (f[i]+=i>=3?g[i-3]:0)%=P,(f[i]+=f[i-1])%=P,(g[i]=g[i-1]+f[i])%=P;
    for(int i=1;i<n;i++) (ans+=1ll*f[i]*(n-1)%P*(n-1)%P)%P;
    for(int i=1;i<n-1;i++) (ans+=1ll*f[i]*(i+1)%P)%P;
    (ans+=1ll*f[n]*n%P)%=P;(ans+=1ll*f[n-1]*(n-1)%P)%=P;printf("%d\n",ans);
}