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<math.h>

typedef long long ll;
#define IMF 1000000007

int main(void){
  ll n;
  scanf("%lld",&n);
  
  ll ans = 0;
  ll dai = 1 , syou = 1 , tyu = 1;
  int count = 0 , kake , tas;
  if(n == 1){
    ans = 0;
  }

  else{
    int count = 0;
    while(count < n){
      dai *= 10;
      dai %= IMF;
      syou *= 8;
      syou %= IMF;
      tyu *= 9;
      tyu %= IMF;
      count ++;
    }
    if(dai <= tyu*2 - syou){
      ans = (IMF+dai) - (tyu * 2 - syou);
    }
    else{
      ans = dai - (tyu * 2 - syou);
    }
  }

  printf("%lld\n",ans);

  return 0;
}