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;

typedef long long LL;

const int MAX_N = 1e6 + 10;
const int MOD = 1e9 + 7;

LL dp[MAX_N], sum;

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);

	LL n;

	cin >> n;
	dp[1] = n, sum = n - 1;
	for (int i = 2; i <= n; i++)
	{
		if (i > 3) sum = (sum + dp[i - 3] - 1) % MOD;

		dp[i] = ((n - 1) * (n - 1) % MOD + dp[i - 1] + sum) % MOD;
	}//for i

	cout << dp[n] << '\n';

	return 0;
}//main