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 N = 1000010, P = 1e9 + 7;
int add(int a, int b) {
    return (a += b) >= P ? a - P : a; 
}
typedef long long ll;
int n;
int dp[N], sum[N];
int main() {
    cin >> n;
    dp[0] = 1;
    sum[0] = 1;
    dp[1] = n;
    sum[1] = n + 1;
    for (int k = 2; k <= n; ++k) {
        dp[k] = (ll)(n - 1) * (n - 1) % P;
        dp[k] = add(dp[k], (sum[k - 1] - dp[k - 2] + P) % P);
        dp[k] = add(dp[k], n - k + 1);
        sum[k] = add(sum[k - 1], dp[k]);
    }
    cout << dp[n] << '\n';
    return 0;
}