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
// KALAM
# include <bits/stdc++.h>

using namespace std;
const int N = 1e6 + 77 , Mod = 1e9 + 7;
int n , dp[N] , ps[N];
int main(){
	scanf("%d" , & n);ps[0] = 1;
	dp[1] = ps[1] = n ;ps[1]++;
	for(int i = 2;i <= n;i++){
		dp[i] = (dp[i - 1] * 1ll + (n - 1) * 1ll * (n - 1) + 1 + n - i) % Mod;
		if(i > 2)dp[i] = (dp[i] + ps[i - 3]) % Mod;
		ps[i] = (ps[i - 1] + dp[i]) % Mod;
	}
	printf("%d" , dp[n]);
	return (0);
}