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 <string.h>
#include <stdlib.h>
 
const long long mod =1000000007;

long long ppow(long long x, long long y){
    long long z;
    z = 1;
    long long i;
    for(i = 0; i < y; i ++){
        z = z * x%mod;
    }
    return z;
}

int main() {
    long long n;
    scanf("%lld", &n);
    long long a =(ppow(10, n)  - ppow(9, n) - ppow(9, n) + ppow(8, n))% mod;
    a = (a + mod)%mod;
    printf("%lld", a);
    return 0;
}