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>
long long int pwo(long long int x,long long int y)
{
    long long int i,a,mod = 1000000000 + 7;
    a = x;
    if(y == 0)
    {
        return 1;
    }
    for(i = 1 ; i < y ; i++)
    {
        x = x*a;
        x = x % mod;
    }
    return x;
}
int main(void)
{
    long long int n,i,j,mod = 1000000000 + 7,sum = 0;
    scanf("%lld",&n);
    sum = pwo(10,n) % mod - 2 * pwo(9,n) % mod + pwo(8,n) % mod;
    sum %= mod;
    
    while(sum < 0)
    {
        sum+= mod;
    }
    printf("%lld\n",sum);
    return 0;
}