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 operator

def ncr(n, r):
    if n < r: return 0
    r = min(r, n-r)
    if r == 0: return 1
    numer = functools.reduce(operator.mul, range(n, n-r, -1), 1)
    denom = functools.reduce(operator.mul, range(1, r+1), 1)
    return numer // denom

def solve():
    n = int(input())
    if n < 2:
        print(0)
    elif n == 2:
        print(2)
    else:
        ans = ncr(n, 2)*2 + 9**(n-2)
        ans %= 10**9+7
        print(ans)
    return 0

if __name__ == "__main__":
    solve()