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 <algorithm>
#include <vector>
#include <map>
#include <set>
#include <string>
#include <iostream>
#define maxn 1000009
using namespace std;
const int MOD = 1e9 + 7;
long long dp[maxn],s[maxn];
int main(){
 long long n;
 scanf("%lld", &n);
 dp[0] = 1;
 s[0]=1;
 for(int i = 1; i <= n; i++){
   dp[i]=(dp[i]+MOD+s[i-1]-dp[i-2])%MOD;
   s[i]=(s[i-1]+dp[i])%MOD;

 }
long long ans=dp[n]+dp[n-1]*(n-1)%MOD;
 for(int i =0; i <= n-2; i++){
  ans += dp[i] * ((i + 1)+(n-1)*(n-1)%MOD)% MOD;
  ans %= MOD;
 }

 cout << ans << endl;
 return 0;
}