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 <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
//二項係数の計算
int nCr(int A, int B) {
    ll ans = 1;
    for (int i = 0; i < B; i++) {
        ans *= A - i;
    }
    for (int i = 0; i < B; i++) {
        ans /= i + 1;
    }
    return ans;
}
long long modpow(long long a, long long n, long long mod) {
    long long res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}
int main() {
    ll N;
    cin>>N;
ll a= modpow(8, N, 1000000007) ;
 ll b=modpow(9, N, 1000000007) ;
 b*=2;
 ll c=modpow(10, N, 1000000007);
  ll d=a+c-b;
  d+=1000000007;
  d%=1000000007;
  cout<<d%1000000007<<endl;
}