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 (Clang 10.0.0) (judge verdict: Wrong Answer)

#include <stdio.h>
int main(void){
    long long int N,ans,i,ansa;
    scanf("%lld",&N);
    ans=1;
    for(i=0;i<N;i++){
        ans=(ans*10)%1000000007;
    }
    ansa=1;
    for(i=0;i<N;i++){
        ansa=(ansa*9)%1000000007;
    }
    ans=(ans-ansa-ansa)%1000000007;
    ansa=1;
    for(i=0;i<N;i++){
        ansa=(ansa*8)%1000000007;
    }
    ans=(ans+ansa)%1000000007;
    printf("%lld\n",ans);
    return 0;
}