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: Accepted)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;

int main() {
    int N;
    cin >> N;
    ull mod = 1000000007;
    if (N == 1) {
        cout << 0 << endl;
    }
    else if (N == 2) {
        cout << 2 << endl;
    }
    else {
        ull ans = 1;
        for (int i=0; i<N; i++) {
            ans *= 10;
            if (ans>=mod) {
                ans %= mod;
            }
        }
        ull del = 1;
        for (int i=0; i<N; i++) {
            del *= 9;
            if (del>=mod) {
                del %= mod;
            }
        }
        ull plus = 1;
        for (int i=0; i<N; i++) {
            plus *= 8;
            if (plus >= mod) {
                plus %= mod;
            }
        }
        del = del * 2;
        ans = ans + mod + mod - del + plus;
        ans %= mod;
        cout << ans << endl;
    }
}