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;
const LL MOD=1000000007LL;
LL dp[1000001]; //dp[i]::=i番目以降の決め方
int main() {
	LL n;
	cin>>n;
	dp[n]=n;
	LL sum=n-1,add=((n-1)*(n-1))%MOD;
	for(int i=n-1;i>=1;i--) {
		dp[i]=(dp[i+1]+add+sum)%MOD;
		sum=(sum+MOD-1)%MOD;
		if(i+2<=n) sum=(sum+dp[i+2])%MOD; else sum=(sum+1)%MOD;
	}
	cout<<dp[1]<<endl;
}