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: Time Limit Exceeded)

#include <stdio.h>
int main(void)
{
    long long int n,i;
    long long int temp=1;
    long long int pp=1;
    long long int kk=1;
    long long int jj;
    scanf("%11d",&n);
    for(i=n;i>0;i--){
        temp=temp*10;
        if (temp>1000000007)
            temp=(temp%1000000007);
    }
    for(i=n;i>0;i--){
        pp=pp*9;
        if (pp>1000000007)
            pp=pp%1000000007;
    }
    for(i=n;i>0;i--){
        kk=kk*8;
        if (kk>1000000007)
            kk=kk%1000000007;
    }
    jj=temp-pp-pp+kk;
    printf("%11d",jj);
    return 0;
}