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(void){
    int N;
    long long a=1,b=1,c=1,mod=pow(10.0,9.0)+7;
    scanf("%d",&N);
    for(int i=0;i<N;i++){
        a=(a*10)%mod;
        b=(b*9)%mod;
        c=(c*8)%mod;
    }

    long long ans=(a-b*2%mod+c)%mod;
    if(N==1)ans=0;

    printf("%lld",ans);

    return 0;
}