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;

int s[1000001],f[1000001],t,n;
const int mod = 1e9+7;
int main() {
	cin >> n;
	if (n == 1) {
		cout << 1;
		exit(0);
	}
	f[0] = 1;
	f[1] = n;
	s[0] = 1;
	s[1] = n+1;
	t = 1ll*(n-1)*(n-1)%mod;
	for (int i = 2; i <=n ;i++) {
	    f[i] = (1ll*t + (n - i + 1) + f[i-1] + (i >= 3 ? s[i-3] : 0))%mod;
	    s[i] = s[i-1] + f[i];
	    if (s[i] > mod) s[i] -= mod;
	}
	cout << f[n];
}