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>
#include <stdlib.h>
#include <math.h>
#include <limits.h>
#include <time.h>
#define ll long long
int main(){
    ll i,n,eight[1000010]={},nine[1000010]={},ten[1000010]={},ans;
    scanf("%lld",&n);
    eight[0]=1;
    nine[0]=1;
    ten[0]=1;
    for(i=0; i<n; i++){
        eight[i+1]=8*eight[i];
        eight[i+1]=eight[i+1]%1000000007;
        nine[i+1]=9*nine[i];
        nine[i+1]=nine[i+1]%1000000007;
        ten[i+1]=10*ten[i];
        ten[i+1]=ten[i+1]%1000000007;
    }
    ans=ten[n]-2*nine[n]+eight[n];
    ans+=2000000014;
    ans=ans%1000000007;
    printf("%lld",ans);
    return 0;
}