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)

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

if N == 1
    puts 0
    exit
end

def modpow x, n
    res = 1
    while n > 0 do
        if n.odd?
            res = res * x % MOD
        end
        x = (x * x) % MOD
        n /= 2
    end
    return res
end

res = modpow(10, N) + modpow(8,N) - 2 * modpow(9,N)
if res <= 0
    puts res + MOD
else
    puts res
end