Problem:
Score : 1000 points

Problem Statement

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.

Sample Input 1

2

Sample Output 1

4

The four sequences that satisfy the conditions are:

1, 1, 1, ...

1, 2, 2, ...

2, 1, 1, ...

2, 2, 2, ...

Sample Input 2

654321

Sample Output 2

968545283

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

const MOD: usize = 1e+9 as usize + 7;
fn main() {
    let n = read::<usize>();
    let mut ans = 0;
    let mut dcnts = vec![0; 2 * n + 10];
    let mut cnt = 1;
    let mut dcnt = 0;
    for i in 0..n * 2 {
        dcnt = (dcnt + dcnts[i]) % MOD;
        cnt = (cnt + dcnt) % MOD;
        if i < n - 1 {
            ans = (ans + cnt * (n - 1) % MOD * (n - 1)) % MOD;
            dcnts[i + 3] = (dcnts[i + 3] + cnt) % MOD;
            dcnts[i + n + 2] = (dcnts[i + n + 2] + MOD - cnt) % MOD;
        } else if i == n - 1 {
            ans = (ans + cnt * n) % MOD;
        } else {
            ans = (ans + dcnt) % MOD;
        }
    }
    println!("{}", ans);
}