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 <math.h>
#include <stdlib.h>
#include <limits.h>
#include <stdbool.h>

#define rep(i, n) for(int i=0; i<(n); ++i)
#define max  200001
#define mod 1000000007

//qsort(str, n, sizeof(int), up_comp);
int up_comp(const void *a, const void *b){return *(int*)a - *(int*)b;}
int down_comp(const void *a, const void *b){return *(int*)b - *(int*)a;}
int int_sort( const void * a , const void * b ) {return strcmp(( char * )a , ( char * )b );}
int count_digit(int a){int i=0;while(a!=0){a=a/10;i++;}return i;}
int euclid( int a, int b ){int temp;if(a<b){temp=a;a=b;b=temp;}if(b<1)return -1;if(a%b==0) return b;return euclid(b,a%b);}

int main(void){
    
    int n;
    long long int ans=0;
    long long int a=1, b=1, c=1;
    
    scanf("%d", &n);
    
    for (int i=1; i<=n; i++) {
        a=a*10%mod;
        b=b*9%mod;
        c=c*8%mod;
        //ans=(ans+a-(2*b%mod)+c)%mod;
    }
    
    ans=(a-(2*b%mod)+c)%mod;
    printf("%lld", ans);
    
    return 0;
}