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 = 1000010, P = 1000000007;
int n, f[maxn];

int main() {
    scanf("%d", &n);
    f[1] = n, f[2] = 1LL * n * n % P;
    for (int i = 3, s = 0; i <= n; i++) {
        (s += f[i - 3]) %= P;
        f[i] = (f[i - 1] + s + 1LL * (n - 1) * (n - 1) + n - i + 2) % P;
    }
    printf("%d\n", f[n]);
    return 0;
}