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 <math.h>

int main(void){
    const long long int MOD = pow(10, 9) + 7;
    int N;
    scanf("%d", &N);
    long long int a = 1, b = 1, c = 1, ans;
    for(int i=0; i<N; i++){
        a *= 10;
        a %= MOD;
        b *= 8;
        b %= MOD;
        c *= 9;
        c %= MOD;
    }
    ans = (a + b - 2 * c) % MOD;
    if(ans < 0) ans += MOD;
    printf("%lld\n", ans);
}