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 <stdio.h>
    #include <string.h>
    #include <stdlib.h>
     
    const long long mod = 1000000007;
    int main() {
        int s;
        scanf("%d", &s);
        int d[s+1];
        d[0] = 1;
        d[1] = 0;
        d[2] = 0;
        int i;
        for(i = 3; i <= s; i ++){
            d[i] = d[i - 1] + d[i - 3];
            d[i]%=mod;
        }
        printf("%d", d[s]);
        return 0;
    }