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 Julia (1.4.0) (judge verdict: Accepted)

const MOD = Int(10^9+7)

function mpow(a, n)
    res = 1
    for i = 1:n
        res *= a
        res %= MOD
    end
    return res
end

function solve()
    N = parse(Int, readline())
    res = mpow(10, N) - mpow(9, N) - mpow(9, N) + mpow(8, N)
    println((res%MOD + MOD)%MOD)
end

solve()