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 Python (3.8.2) (judge verdict: Runtime Error)

import math
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
N = int(input())

all = 0
for i in range(2, N//2+1):
    basyo = combinations_count(N, i)  # iとN-iの時、値が同じ

    zero_iti  = 2 ** (3 * N - 2 * i - 1)  # i=iの時
    zero_iti2 = 2 ** (N + 2 * i - 1)      # i=N-iの時

    all += basyo * (zero_iti + zero_iti2)

if S % 2 == 0:  # i = Nが無いので足す
    basyo = combinations_count(N, N)
    zero_iti = 2 ** (N - 1)
    all += basyo * zero_iti

if S % 2 == 1:  # i = N-1も無いので足す
    basyo = combinations_count(N, N)
    zero_iti = 2 ** (N - 1)
    all += basyo * zero_iti

    basyo = combinations_count(N, N - 1)
    zero_iti = 2 ** (N - 2)
    all += basyo * zero_iti

print(int(all % (10**9+7)))