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: Wrong Answer)


import math

mod=10**9+7

N=int(input())

if(N==1):
    print(0)
else:

    if(N-2>10):
        a=10**(N-2)%mod
        b=math.factorial(N) //  math.factorial(N-2)
        c1=b*a%mod
        print(c1)
    else:
        a=10**(N-2)
        b=math.factorial(N) //  math.factorial(N-2)
        c=b*a
        print(c)