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>

const int Mod = 1000000007;

int main()
{
	int N;
	scanf("%d", &N);
	if (N == 1) {
		printf("0\n");
		fflush(stdout);
		return 0;
	}
	
	int i;
	long long pow[3][1000001];
	for (i = 1, pow[0][0] = 1, pow[1][0] = 1, pow[2][0] = 1; i <= N; i++) {
		pow[0][i] = pow[0][i-1] * 10 % Mod;
		pow[1][i] = pow[1][i-1] * 9 % Mod;
		pow[2][i] = pow[2][i-1] * 8 % Mod;
	}		
	
	printf("%lld\n", (pow[0][N] - pow[1][N] * 2 + pow[2][N] + Mod * 2) % Mod);
	fflush(stdout);
	return 0;
}