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>
#include <vector>
#include <algorithm>
#include <math.h>
#include <string>
#define ll long long

using namespace std;
typedef pair<int, int> P;

ll mod = 1000000007;

int main()
{
    ll n;
    cin >> n;
    if (n == 1)
    {
        cout << 0 << endl;
        return 0;
    }
    else
    {
        ll a = 1, b = 1, c = 1;
        for (int i = 0; i < n; i++)
        {
            a *= 10ll;
            a %= mod;
            c *= 9ll;
            c %= mod;
            b *= 8ll;
            b %= mod;
        }
        cout << (a - 2 * c + b) % mod << endl;
    }
    return 0;
}