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;

const long MOD = 1000000007;

long dp[1000000];
long dp_sum;

int main(){
    long n;
    cin >> n;
    dp[0] = n;
    dp[1] = (n*n)%MOD;
    dp_sum = 0;
    for(int i = 2; i <= n-1; i++){
        dp[i] = dp[i-1]+dp_sum+(n-1)*(n-1)+(n-(i-1));
        dp[i] %= MOD;
        dp_sum += dp[i-2];
        dp_sum %= MOD;
    }
    cout << dp[n-1] << endl;
}