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: Accepted)

#include<stdio.h>
#include<string.h>

#define mod 1000000007

long long int multiple(long long int target, long long int p)
{
    long long int curretn_answer = 0;

    if (p == 0)
    {
        return 1;
    }

    if (p%2 == 0)
    {
        curretn_answer = multiple(target, (p/2))*multiple(target, (p/2));
        curretn_answer %= mod;
    } else {
        curretn_answer = multiple(target, ((p-1)/2))*multiple(target, ((p-1)/2));
        curretn_answer %= mod;
        curretn_answer *= target;
        curretn_answer %= mod;
    }

    return curretn_answer;
}

int main()
{
    long long int n, answer = 0;

    scanf("%lld", &n);

    answer = (multiple(10, n) - multiple(9, n) + mod);
    answer %= mod;
    answer *= 2;

    answer -= (multiple(10, n) - multiple(8, n) + mod)%mod;

    answer += mod;
    answer %= mod;

    printf("%lld", answer);

    return 0;
}