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
//http://arc071.contest.atcoder.jp/tasks/arc071_d
#include <bits/stdc++.h>

using namespace std;

const int maxn = 1000010;
const long long  base = 1e9+7;

long long f[maxn],n;

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin>>n;
    f[1]=n;
    f[2]=n*n%base;
    int sum=0;
    for (int i=3;i<=n;i++) {
        if (i>3) sum = (sum+f[i-3])%base;
        f[i]=(f[i-1] + (n-1)*(n-1)%base + sum + (n-1 - (i-3))) % base;
    }
    cout<<f[n];
}
