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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

import sys
sys.setrecursionlimit(250000)

from scipy.special import comb
# a = comb(n, r)

def main():
    # a,b,c,d = map(int, input().split())
    n = int(input())

    sum = 10**n - 9**n*2 + 8**n
    # temp = (10 ** 9 + 7)
    # sum = 0
    # if n >= 2:
    #     for i in range(2, n+1):
    #         a = int(comb(i, 2)) * 2
    #         a = (a * 8**(i-2)) % temp
    #         sum = sum + a
    # else:
    #     print(0)

    print(sum % (10 ** 9 + 7))

main()