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;

const int MaxN = 1000005;
const long long Mod = 1000000007;

long  long n;
long long f[MaxN];

int main() 
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cin >> n;
    long long sum = n;
    f[n] = n;
    for (int i = n - 1; i >= 1; --i)
    {
        f[i] = (sum - f[i + 2] + i + (i != n - 1) + (n - 1) * (n - 1) + Mod * Mod) % Mod;
        sum = (sum + f[i])%Mod;
    }
    cout << f[1];
    return 0;
}