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>
#define maxn 1010000
#define mod 1000000007
using namespace std;
int ans,dp[maxn],n,s[maxn];
int main(){
	scanf("%d",&n);
	dp[1]=n,s[1]=dp[1];
	dp[2]=1ll*n*n%mod,s[2]=(dp[1]+dp[2])%mod; 
	for(int i=3;i<=n;++i){
		dp[i]=(dp[i-1]+s[i-3]+1ll*(n-1)*(n-1)+n-i+2)%mod;
		s[i]=(s[i-1]+dp[i])%mod;
	}
	printf("%d",dp[n]);
}