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
//In The Name of Allah
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N = 1e6 + 10;
const ll mod = 1e9 + 7;

ll dp[N];

int main(){
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    ll n;
    cin >> n;
    dp[0] = 1;
    dp[1] = n;
    ll ps = n - 1;
    for (ll i = 2; i <= n; i ++){
        dp[i] = (dp[i - 1] + (n - 1) * (n - 1) % mod + ps) % mod;
        ps = (ps + dp[i - 2] - 1) % mod;
    }
    dp[n] = (dp[n] + mod) % mod;
    cout << dp[n];
    return 0;
}
