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 <stdlib.h>
#include <string.h>
#include <math.h>
#define rep(i,l,r)for(int i=(l);i<(r);i++)

int main(void){
  int n;
  scanf("%d",&n);
  if(n<2){
    printf("0");
    return 0;
  }
  else{
    long long int ten=1,nine=1,eight=1,MOD = 1000000007;
    rep(i,0,n){
      ten = ten*10;
      ten = ten%MOD;
      nine = nine*9;
      nine = nine%MOD;
      eight = eight*8;
      eight = eight%MOD;
    }
    eight = eight + ten - nine - nine;
    if(eight<0) eight += 1000000007;
    eight = eight%MOD;
    printf("%lld",eight);
  return 0;
}}