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<iostream>
#include<cstdio>
//This code is written by Itst
using namespace std;

const int MAXN = 1e6 + 7 , MOD = 1e9 + 7;
int N , dp[MAXN];

int main(){
	cin >> N;
	dp[N] = N; dp[N - 1] = (1ll * N * N + dp[N]) % MOD;
	for(int i = N - 2 ; i > 0 ; --i)
		dp[i] = (dp[i + 1] - dp[i + 2] + (N - 1ll) * (N - 1) + dp[i + 3] + dp[i + 1] + i + 1 + MOD) % MOD;
	cout << (dp[1] - dp[2] + MOD) % MOD;
	return 0;
}
