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 mod = 1e9 + 7;

void add(int &x,int y) {
	x += y; if (x >= mod) x -= mod;
}

int mul(int x,int y) {
	return 1LL * x * y % mod;
}

int n;
int f[1000005];

int main() {
	ios_base::sync_with_stdio(false);
	cin >> n;
	f[0] = 1; f[1] = n; f[2] = mul(n, n);
	int sum = f[0] + f[1] + f[2];
	while (sum >= mod) sum -= mod;
	for (int i = 3; i <= n; ++i) {
		add(f[i], mul(n - 1, n - 1));
		add(f[i], sum);
		add(f[i], mod - f[i - 2]);
		add(f[i], n - i + 1);
		add(sum, f[i]);
	}
	cout << f[n] << '\n';
}
