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)

local mod=1000000007
local function powmod(x,n)
    local a=1
    for i=1,n do
        a=(a*x)%mod
    end
    return a
end

----------

local n=io.read("n")
local total=powmod(10,n)
local zorn=powmod(9,n)
local zandn=powmod(8,n)
print((total-zorn-zorn+zandn)%mod)