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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

process.stdin.resume();
process.stdin.setEncoding('utf-8');
 
let inputString = '';
let currentLine = 0;
 
process.stdin.on('data', inputStdin => {
    inputString += inputStdin;
});
 
process.stdin.on('end', _ => {
    inputString = inputString.split(/\n/);
    main();    
});
 
function readLine() {
    return inputString[currentLine++];
}

const mod = Math.pow(10, 9) + 7
function main() {
  const n = Number(readLine())
  let tens = 1
  let nines = 2
  let eights = 1
  for (let _ = 0; _ < n; _++) {
    tens = (tens * 10) % mod
    nines = (nines * 9) % mod
    eights = (eights * 8) % mod
  }
  const total = tens - nines + eights
  console.log(total >= 0 ? total % mod : total + mod)
}