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(){
	int n;
	scanf("%d", &n);
	if(n==1) {
		printf("0");
		return 0;
	}
	long long a = 1;
	long long b = 1;
	long long c = 1;
	long long ans;
	for(int i=0; i<n; i++) {
		a *= 10;
		a%=1000000007;
		b *= 9;
		b%=1000000007;
		c *= 8;
		c%=1000000007;
	}
	ans = a - 2 * b + c;
	ans = (ans + 100000007) % 1000000007;
	printf("%lld", ans);
	return 0;
}