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 <cstdio>
#define mod 1000000007
long long pow(long long a,int n){//注意要用快速幂！
    long long base=a,ans=1;
    while(n){
        if(n&1) ans=ans*base%mod;
        base=base*base%mod,n>>=1;
    }
    return ans;
}
int main(){
    int n;scanf("%d",&n);
    printf("%lld\n",(pow(10,n)-2*pow(9,n)+pow(8,n)+mod)%mod);
    return 0;
}