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 int long long
#define MOD 1000000007
using namespace std;

signed main(){
	int n,dp[1000010] = {1,1,1,2},ans = 0;
	cin >> n;
	for(int i = 4;i <= n;i++) dp[i] = (dp[i - 4] + dp[i - 2] + dp[i - 1]) % MOD;
	for(int i = 0;i < n - 2;i++) (ans += dp[i] * ((n - 1) * (n - 1) % MOD + i + 2)) %=  MOD;
	(ans += dp[n - 2] * ((n - 1) * (n - 1) % MOD + n - 1)) %= MOD;
	(ans += dp[n - 1] * n) %= MOD;
	cout << ans << endl;
	return 0;
}