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>

using namespace std;
long long dp[2000010] = {},sum[2000010] = {},mod = 1000000007;
int main(){
	long long i,n;
	cin >> n;
	for(i=2*n;i>=n+1;i--){
		dp[i] = 1;
		sum[i] = sum[i+1] + dp[i];
	}
	dp[n] = n; sum[n] = sum[n+1] + dp[n];
	for(i=n-1;i>=1;i--){
		(dp[i] += (sum[i+1] - sum[i+n+2]) - dp[i+2] + (n-1)*(n-1) + mod) %= mod;
		sum[i] = (sum[i+1] + dp[i])%mod;
	}
	cout << dp[1] << endl;
}