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 int lli;

const lli MOD = 1e9 + 7;
const lli N = 1e6 + 5;
lli n;
lli dp[N+1];

int main() {
	cin >> n;

	dp[1] = n;
	dp[2] = n*n % MOD;
	lli sum = dp[1] + dp[2];
	sum %= MOD;
	for(lli i = 3; i <= n; i++) {
		dp[i] = (n-1)*(n-1) + sum - dp[i-2] + n - i + 2;
		dp[i] += MOD;
		dp[i] %= MOD;
		sum += dp[i];
		sum %= MOD;
	}
	cout << dp[n] << endl;

	return 0;
}