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 LL;
#define repp(i,a,b) for(int i = (int)(a) ; i < (int)(b) ; ++i)
#define repm(i,a,b) for(int i = (int)(a) ; i > (int)(b) ; --i)

int main(){
	int N; cin >> N;
	const LL mod = 1e9+7;
	vector<LL> dp(N+1,1);
	dp[1] = N;
	LL s = N+1;
	repp(i,1,N){
		dp[i+1] = ((LL)(N-1)*(N-1)+s-dp[i-1]+N-i)%mod;
		s = (s+dp[i+1])%mod;
	}
	cout << (dp[N]+mod)%mod << endl;
	return 0;
}
