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;

#define int long long
int MOD = 1000000007;
signed main() {
	int n;
	cin >> n;
	if (n == 1) {
		cout << 1 << endl; return 0;
	}
	if (n == 2) {
		cout << 4 << endl; return 0;
	}
	if (n == 3) {
		cout << 15 << endl; return 0;
	}
	vector<int> dp(n+5);
	dp[0] = n-1;
	dp[1] = n*n - n;
	dp[2] = n*n - n;
	int sum = dp[0] + dp[1] + dp[2];
	for (int i = 3; i < n; i++) {
		dp[i] = ((sum - dp[i - 2]) + MOD) % MOD;
		sum = (sum + dp[i]) % MOD;
	}
	cout << ((sum+1) % MOD) << endl;
	return 0;
}