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 Ruby (2.7.1) (judge verdict: Accepted)

# frozen_string_literal: true

n = gets.to_i

MOD = 10**9 + 7

if n == 1
  puts 0
  exit
end

# nP2 * 10**(n - 2)

s = 1
n.times do
  s *= 10
  s %= MOD
end

z = 2
n.times do
  z *= 9
  z %= MOD
end

e = 1
n.times do
  e *= 8
  e %= MOD
end

puts (s - z + e) % MOD