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: Accepted)

#include<stdio.h>
#define MOD 1000000007LL

long long int pow( long long int b, long long int i ){
  long long int r = 1;
  while( i ){
    if( i%2 ){
      r *= b;
      r %= MOD;
    }
    b *= b;
    b %= MOD;
    i >>= 1;
  }
  return r;
}

int main(){
  long long int N;
  scanf("%lld", &N);
  long long int ans = pow(10,N) - 2*pow(9,N) + pow(8,N);
  ans = (ans+MOD*100) % MOD;
  printf("%lld\n", ans);
}