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(void)
{
    int i,N;
    scanf("%d", &N);
    long int a = 1;
    long int aa = 1;
    long int aaa = 1;
    for (i = 1;i <= N;i++)
    {
        a = a * 10;
        a = (a % 1000000007);
    }
    for (i = 1;i <= N;i++)
    {
        aa = aa * 8;
        a = (a % 1000000007);
    }
    for (i = 1;i <= N;i++)
    {
        aaa = aaa * 9;
        a = (a % 1000000007);
    }
    aaa = aaa - aa;
    a = a - aaa - aaa - aa;
    a = (a % 1000000007);
    printf("%ld", a);
    return 0;
}