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>
#define rep(i,N) for (int i = 0; i < (N); ++i)
#define all(v) v.begin(), v.end()
using namespace std;
using ll = long long;
using P = pair<int, int>;
const int inf{int(1e9)};
const int mod = 1000000007;

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(void){
  int N;
  cin >> N;
  ll a = modpow(10, N, 1000000007);  // 10^n
  ll b = modpow(9, N, 1000000007);  // 9^n
  ll c = modpow(8, N, 1000000007);  // 8^n
  ll ans = (a - (2 * b - c)) % mod;
  cout << ans << endl;
  return 0;
}