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)

import math
from sys import stdin

N = int(input())
MOD = 1000000007

def solve(N):
    res=1
    zn=1
    zz=1
    zo=1
    for i in range(N):
        res=(res*10)%MOD
    for i in range(N):
        zn=(zn*9)%MOD
    for i in range(N):
        zz=(zz*9)%MOD
    for i in range(N):
        zo=(zo*8)%MOD
    zx = ((zz + zn)%MOD - zo) % MOD
    return (res-zx)%MOD

if(N<2):print(0)
else: print(solve(N))