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 <iostream>
     
    using namespace std;
     
    constexpr long long MOD = 1000000007;
     
    long long pow_mod(long long b, long long e)
    {
    	long long res = 1;
    	for (long long i = 0; i < e; i++)
    		res = (res * b) % MOD;
    	return res;
    }
     
    int main()
    {
    	long long n;
    	cin >> n;
    	long long res = ((pow_mod(10, n) - (2ll * pow_mod(9, n)) % MOD) % MOD + pow_mod(8, n)) % MOD;
        cout << res << endl;
    	return 0;
    }