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<iostream>
#include<algorithm>
using namespace std;
long long a[3000000], mod = 1000000007, cnt;
int main() {
	int n; cin >> n;
	a[0] = 0; a[1] = 1; a[2] = 1; a[3] = 1;
	for (int i = 4; i <= 2000000; i++) { a[i] = a[i - 1] + a[i - 2] + a[i - 4]; a[i] %= mod; }
	for (int i = 1; i < n; i++) { cnt += (a[i] * (n - 1)); cnt %= mod; }
	for (int i = 1; i < n; i++) { cnt += (((a[i] * (n - 2)) + a[i + 1]) % mod)*(n - 1); cnt %= mod; }
	cout << (cnt + n) % mod << endl;
	return 0;
}