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)

class ModInt
	@@mod = 1_000_000_007

	def initialize(n)
		@n = n.to_i % @@mod
	end

	def self.zero
		ModInt.new(0)
	end

	def self.mod=(m)
		@@mod = m.to_i
	end

	def +@
		self
	end

	def -@
		ModInt.new(n != 0 ? @@mod - @n : 0)
	end

	def +(m)
		ModInt.new(@n + m.to_i % @@mod)
	end

	def -(m)
		ModInt.new(@n - m.to_i % @@mod)
	end

	def *(m)
		ModInt.new(@n * m.to_i % @@mod)
	end

	def /(m)
		raise DivisionByZeroError.new if m == 0
		a, b, u, v = m.to_i, @@mod, 1, 0
		while b != 0
			t = a / b
			a -= t * b
			a, b = b, a
			u -= t * v
			u, v = v, u
		end
		ModInt.new(@n * u)
	end

	def **(m)
		t, res = self, ModInt.new(1)
		while m > 0
			res *= t if m.odd?
			t *= t
			m >>= 1
		end
		res
	end

	def ==(m)
		@n == m.to_i
	end

	def !=(m)
		@n != m.to_i
	end

	def succ
		self + 1
	end

	def pred
		self - 1
	end

	def to_i
		@n
	end

	def to_s
		@n.to_s
	end
end

n = gets.to_i
puts ModInt.new(10)**n - ModInt.new(9)**n * 2 + ModInt.new(8)**n