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)

const mod = BigInt(10**9 + 7)

const pow = (x, n) => {
  let r = 1n

  for (let i=0; i<n; i++)
    r = r * x % mod

  return r
}

const main = (input) => {
  const n = BigInt(input.trim())

  let a = pow(10n, n)
  let bc = pow(9n, n)
  let d = pow(8n, n)

  const ans = (a-bc-bc+d) % mod
  return console.log(`${(ans + mod) % mod}`)
}

process.env.MYTEST
  ? (process.env.MYTEST === 'test' ? test() : main(require('fs').readFileSync('dev/stdin', 'utf8')))
  : main(require('fs').readFileSync('/dev/stdin', 'utf8'))