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)

const mod = 10**9 +7;

function pow (x,y){
    var r = 1;
    for (var i=1; i<=y; i++){
        r = (r * x) % mod;
    }
    return r;
};


function Main (input){
    const [N] = input.trim().split(' ').map(x => parseInt(x));
    var count = pow(10,N)-(pow(9,N)*2)+pow(8,N);
    count = count % mod;
    count = (count + mod) % mod;
    console.log(count)
};


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