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: Wrong Answer)

local n = io.read("n")

--nC1 * (n - 1)C1 10^(n - 2)

if n == 1 then
	print(0)
	os.exit()
end

local ten_pow, nin_pow = 1, 0
local eig_pow_t, nin_pow_t = {8}, {9}
for i = 2, n do
	eig_pow_t[i] = (eig_pow_t[i - 1] * 8) % 1000000007
	nin_pow_t[i] = (nin_pow_t[i - 1] * 9) % 1000000007
end

for i = 1, n do
	ten_pow = (ten_pow * 10) % 1000000007
end
print(ten_pow)
for i = 1, n do
	print(eig_pow_t[i - 1], nin_pow_t[n - i])
	local num = nin_pow + ((eig_pow_t[i - 1] or 1) * (nin_pow_t[n - i] or 1)) % 1000000007
	nin_pow = num % 1000000007
end
print(nin_pow)
print(eig_pow_t[n])
local out = ((nin_pow * 2) % 1000000007 + eig_pow_t[n]) % 1000000007
out = out < 0 and out + 1000000007 or out
out = ten_pow - out < 0 and ten_pow - out + 1000000007 or ten_pow - out
print(out)