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: Accepted)

#                               #
    # author : samars_diary #
    # 16-09-2020 │ 18:28:11 #
#                               #

import sys, os.path, math

#if(os.path.exists('input.txt')):
    #sys.stdin = open('input.txt',"r")
    #sys.stdout = open('output.txt',"w")

sys.setrecursionlimit(10 ** 5)

def mod(): return 10**9+7
def i(): return sys.stdin.readline().strip()
def ii(): return int(sys.stdin.readline())
def li(): return list(sys.stdin.readline().strip())
def mii(): return map(int, sys.stdin.readline().split())
def lii(): return list(map(int, sys.stdin.readline().strip().split()))

#print=sys.stdout.write

def solve():
    a=ii();print((pow(10,a,mod())+pow(8,a,mod())-2*pow(9,a,mod()))%mod())
for _ in range(1):
    solve()