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<bits/stdc++.h>
 
using namespace std;
 
const long long mod = 1e9 + 7;
 
long long n;
 
int main() {
  scanf("%lld", &n);
  
  long long sol = 1, a = 1, b = 1;
  
  for (int i = 0; i < n; i++) {
  	sol *= 10;
  	sol %= mod;
    a *= 9;
    a %= mod;
    b *= 8;
    b %= mod;
  }
  
  printf("%lld", (sol - 2 * a + b + mod) % mod);
  
  return 0;
}