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: Wrong Answer)

def choose(n, r)
  1 if r == 0 or r == n

  # store C(n,r) in a matrix
  c = Array.new(n+1).map{Array.new(r+1,0)}
  i,j = 0

  for i in 0..n
    # C(i,0) = 1 for i = 0...n
    c[i][0] = 1
  end
  for j in 0..r
    # if n = 0, C(n,r) = 0 for all 'r'
    c[0][j] = 0
  end

  for i in 1..n
    for j in 1..r
      if i == j
        # C(n,n) = 1
        c[i][j] = 1
      elsif j > i
        # case when r > n in C(n,r)
        c[i][j] = 0
      else
        # apply the standard recursive formula
        c[i][j] = c[i-1][j-1] + c[i-1][j]
      end
    end
  end

  return c[n][r]
end

n = 869121
r = 2
comb = choose(n,r)
puts comb % (10**9 + 7) / 272