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>
#define mod 1000000007
#define ll long long
ll sp(ll a,ll b)
{
  ll c=1;
  while(a)
  {
    if(a&1){c*=b;c%=mod;}
    b*=b;
    b%=mod;
    a>>=1;
  }
  return c;
}
int main()
{
  ll n,ans;
  scanf("%lld",&n);
  if(n==1)ans=0;
  else if(n==2)ans=2;
  else {
    ans=(sp(n,10)-2*sp(n,9)+mod)%mod;
      ans+=sp(n,8)%mod;
  }
  printf("%lld\n",ans%mod);
}