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>
#include <string.h>
#include <math.h>
#define MOD 1000000007
int main(int argv,char* argc[]){
    long long n,ans=1,def1=1,def2=1;
    scanf("%lld",&n);
    if(n==1){
        printf("0");
        return 0;
    }
    if(n==2){
        printf("2");
        return 0;
    }
    for(int i=0;i<n;i++){
        ans*=10;
        ans%=MOD;
        def1*=9;
        def1%=MOD;
        def2*=8;
        def2%=MOD;
    }
    ans-=(def1*2-def2);
    ans=(ans+MOD)%MOD;
    ans=(ans+MOD)%MOD;
    printf("%lld",ans);
    
    return 0;
}