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: Accepted)

#include <stdio.h>

long long DIV = 1000000007;

long long rest_div(int x, int y)
{
        int i;
        long long ret = 1;

        for (i = 0; i < y; i++)
        {
                ret = ret * x % DIV;
        }
        return (ret);
}

int main(void)
{
        int n;
        long long ans = 0;

        scanf("%d", &n);
        if (n == 1)
        {
                printf("%d\n", 0);
                return (0);
        }
        ans = rest_div(10, n) - rest_div(9, n) - rest_div(9, n) + rest_div(8, n);
        ans = ans%DIV;
        ans = (ans + DIV) % DIV;
        printf("%lld\n", ans);
        return (0);
}