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,i;
	scanf("%d",&n);
	long long int x10=1,x9=1,x8=1;
	for(i=0;i<n;i++)
	{
		x10=(10*x10)%1000000007;
		x9=(9*x9)%1000000007;
		x8=(8*x8)%1000000007;
	}
	printf("%lld",(x10-2*x9+x8)%1000000007);
	return 0;
}