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>
typedef long long ll;
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
	
using namespace std;
const int MAX_N=1e6;
const ll MOD=1e9+7;
ll n;
ll dp[MAX_N+1];
int main(){
	cin>>n;
	dp[0]=1;
	dp[1]=n;
	dp[2]=n*n%MOD;
	ll sm=(1+n+n*n)%MOD;
	FOR(i,3,n+1){
		ll v=(sm-dp[i-2]+MOD)%MOD;
		v+=n-i+1;
		v%=MOD;
		v+=(n-1)*(n-1)%MOD;
		v%=MOD;
		dp[i]=v;
		sm+=v;
		sm%=MOD;
	}
	cout<<dp[n]<<endl;
	return 0;
}