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 < (int)n; ++i)

typedef long long ll;

const ll MOD = 1e9 + 7;

using namespace std;

ll powmod(int a, int b) {
    ll val = 1;
    REP(_, b) {
        val *= a;
        val %= MOD;
    }
    return val;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(NULL);

    int N;
    cin >> N;

    ll cnt = powmod(10, N) - powmod(9, N) - powmod(9, N) + powmod(8, N);
    cnt %= MOD;

    cout << cnt << endl;
}