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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

function Main(input) {

	// 1行目がinput[0], 2行目がinput[1], …に入る
	input = input.split("\n");
    
    let N = Number(input[0]);
    
    let pow_10 = myPow(10n,BigInt(N),10n ** 9n + 7n);
    let pow_9 = myPow(9n,BigInt(N),10n ** 9n + 7n);
    let pow_8 = myPow(8n,BigInt(N),10n ** 9n + 7n);
    
    let ans = pow_10 - 2n * pow_9 + pow_8;
    while(ans < 0n) ans += (10n ** 9n + 7n);
    
    console.log(ans.toString());
    
}

function myPow(x, n, m){
  if(n == 0)
    return 1n;
  if(n % 2n == 0)
    return myPow(x * x % m, n / 2n, m);
  else
    return x * myPow(x, n - 1n, m) % m;
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));