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>
const long long int mod =1000000000+7;
int main()
{
    long long int n,i;
    long long int ans=1,ans1=1;
    scanf("%lld",&n);
    if(n<2)
    {
        ans=0;
    }
    else
    {
        for(i=0;i<n;i++)
        {
            ans*=10;
            ans%=mod;
        }
        for(i=0;i<n;i++)
        {
            ans1*=9;
            ans1%=mod;
        }
        //printf("%lld %lld\n",ans,ans1);
        ans-=ans1;
        ans%=mod;
        ans-=ans1;
        ans%=mod;
        ans1=1;
        ans=ans%mod;
        //printf("%lld\n",ans);
        for(i=0;i<n;i++)
        {
            ans1*=8;
            ans1%=mod;
        }
        ans+=ans1;
        ans%=mod;
    }
    printf("%lld\n",ans%mod);
    return 0;
}