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>
#include <stdlib.h>

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