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<stdlib.h>
#include<string.h>
#include<stdbool.h>
#include<math.h>
#include<limits.h>
#define MOD 1000000007

typedef long long ll;

int max(int a,int b){
    if(a>b) return a;
    else return b;
}

int min(int a,int b){
    if(a<b) return a;
    else return b;
}

/*qsort(array,num_of_index,sizeof(int),compare_int); */
 int compare_int(const void *a,const void *b){
     return *(int*) a - *(int *) b; 
 } 

ll calc(ll num,ll len){
    ll tmp=1;
    for(ll i=0;i<len;i++){
        tmp *= num;
        tmp %= MOD;    
    }
    return tmp;
}
 
int main(){
    ll N;    
    scanf("%lld",&N);
    ll ans = 10000*MOD + calc(10,N) + calc(8,N) - 2*calc(9,N);
    ans %= MOD;
    printf("%lld",ans);
}