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)

def pow(x, n, mod)
  ans = 1
  while n > 0
    ans = ans * x % mod if n.odd?
    x = x * x % mod
    n >>= 1
  end
  ans
end

N = gets.to_i
MOD = 10 ** 9 + 7

ans = pow(10, N, MOD) - 2 * pow(9, N, MOD) + pow(8, N, MOD)
ans += MOD if ans < 0
ans += MOD if ans < 0

puts ans