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>
#define mod 1000000007
using namespace std;
int n, dp[1000007], sum;
int main()
{
	cin >> n;
	dp[n] = n;
	dp[n - 1] = 1LL * n * n % mod;
	for (int i = n - 2; i >= 1; i--)
	{
		sum = (sum + dp[i + 3]) % mod;
		dp[i] = (sum + 1LL * (n - 1) * (n - 1) % mod + dp[i + 1] + i + 1) % mod;
	}
	cout << dp[1] << endl;
	return 0;
}