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>

typedef long long ll;
const int N = 1000054, mod = 1000000007;

int n;
int f[N];
ll F[N];

int main() {
	int i; ll t;
    scanf("%d", &n), t = (n - 1ll) * (n - 1ll) % mod;
    for (F[n] = f[n] = n, i = n - 1; i; --i)
    	f[i] = (f[i + 1] + t + i + (i != n - 1) + F[i + 3]) % mod,
    	F[i] = F[i + 1] + f[i];
    printf("%d\n", f[1]);
    return 0;
}