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;

long long int N, dp[1919810][2], i, ans, con;

static inline long long dpt(int b){
    return ((b - 3 >= 0) ? dp[b - 3][1] + N - b + 1 : N - 1) % 1000000007;
}

int main(){
    scanf("%lld", &N);
    ans = con = (N - 1) * (N - 1) % 1000000007;
    dp[0][0] = N;
    dp[0][1] = N;
    for(i = 1; i <= N; ++i){
        dp[i][0] = (dp[i - 1][0] + con + dpt(i)) % 1000000007;
        dp[i][1] = (dp[i - 1][1] + dp[i][0]) % 1000000007;
    }
    cout << dp[N - 1][0] << endl;
    return 0;
}
