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<math.h>
int main()
{
    int N;
    scanf("%d",&N);
    long long x,y,z=1000000007;
    x=N*(N-1);
    while(x>z)
    {
        x=x-z;
    }
    
    y=1000000000000000000;
    while(y>z)
    {
        y=y-z;
    }
    while(N-2>18)
    {
        x=x*y;
        while(x>z)
        {
            x=x-z;
        }
        N=N-18;
    }
    y=pow(10,N-2);
    while(y>z)
    {
        y=y-z;
    }
    x=x*y;
    while(x>z)
    {
        x=x-z;
    }

    printf("%lld",x);
    return 0;
}