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: Accepted)

#include<stdio.h>
long long int modpow(long long int a, long long int n, long long int p)
{
	long long int res = 1;
	while (n > 0)
	{
		if (n % 2 > 0)
			res = res * a % p;
		a = a * a % p;
		n /= 2;
	}
	return res;
}
int main()
{
	long long int n;
	scanf("%lld", &n);
	long long int p = 1000000007;
	printf("%lld\n", ((modpow(10, n, p) - 2 * modpow(9, n, p) % p) % p + modpow(8, n, p) + p) % p);
	return 0;
}