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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int		main(void)
{
	long		N;
	long		i;
	long		ten_n;
	long		nine_n;
	long		eight_n;

	scanf("%ld", &N);
	ten_n = 1;
	nine_n = 2;
	eight_n = 1;
	for (i = 0; i < N; i++){
		ten_n *= 10;
		nine_n *= 9;
		eight_n *= 8;
		ten_n %= 1000000007;
		nine_n %= 1000000007;
		eight_n %= 1000000007;
	}
	printf("%ld\n", (ten_n - nine_n + eight_n));
	return (0);
}