Problem:
Score : 300 points

Problem Statement

How many integer sequences A_1,A_2,\ldots,A_N of length N satisfy all of the following conditions?

0 \leq A_i \leq 9

There exists some i such that A_i=0 holds.

There exists some i such that A_i=9 holds.

The answer can be very large, so output it modulo 10^9 + 7.

Constraints

1 \leq N \leq 10^6

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer modulo 10^9 + 7.

Sample Input 1

2

Sample Output 1

2

Two sequences \{0,9\} and \{9,0\} satisfy all conditions.

Sample Input 2

1

Sample Output 2

0

Sample Input 3

869121

Sample Output 3

2511445

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;
const MOD: isize = 1_000_000_007;

fn main() {
  input! {
    n: usize
  }
  
  if n == 1 {
    println!("0");
    return
  }
  
  let mut result: isize = 1;
  for i in 0..n {
    result *= 10;
    result %= MOD;
  }
  
  let mut a: isize = 1;
  for i in 0..n {
    a *= 9;
    a %= MOD;
  }
  
  let mut b: isize = 1;
  for i in 0..n {
    b *= 9;
    b %= MOD;
  }
  
  let mut c: isize = 1;
  for i in 0..n {
    c *= 8;
    c %= MOD;
  }
  
  let mut minus = (a + b) % MOD;
  minus = (minus - c) % MOD;
  if minus < 0 {
    minus += MOD;
  }
  
  result = (result - minus) % MOD;
  if result < 0 {
    result += MOD;
  }
  
  println!("{}", result);
}