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;
typedef long long ll;
typedef pair<int, int> pii;
const int mod = 1000000007;

int main() {
    ios::sync_with_stdio(false);
    ll n, d[1000006] = {}, c = 0;
    cin >> n;
    d[0] = 1; d[1] = n; d[2] = n * n % mod; c = n - 1;
    for (int i = 3; i <= n; i++) {
        c = (c + d[i - 3] - 1) % mod;
        d[i] = (d[i - 1] + (n - 1) * (n - 1) + c) % mod;
    }
    cout << d[n] << '\n';
}
