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>
#include <stdlib.h>
#include <math.h>

int main(void){
	int N,i,a;
	a=(int)pow(10,9)+7;
	scanf("%d",&N);
	long long int I=10,J=9,K=8,M;
	for (i=1;i<N;i++){
		I=(I*10) % a;
	}
	for (i=1;i<N;i++){
		J=(J*9) % a;
	}
	for (i=1;i<N;i++){
		K=(K*8) % a;
	}
	M = I-(2*J-K);
	while (M>=0)
	{
		M=M+a;
	}
	
	printf("%lld",M);
	return 0;
}