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 Lua (Lua 5.3.5) (judge verdict: Accepted)

-- Vicfred
-- https://atcoder.jp/contests/abc178/tasks/abc178_c
-- math

function binpow(a, b, m)
    a = a % m
    res = 1
    while b > 0 do
        if (b % 2) == 1 then
            res = (res * a) % m
        end
        a = (a * a) % m
        b = b // 2
    end

    return res
end

mod = 1000000007

n = io.read("*n")

ans = binpow(10, n, mod) - binpow(9, n, mod) - binpow(9, n, mod) + binpow(8, n, mod)
ans = ans + mod
ans = ans % mod
print(ans)