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 min3(a, b, c) min(a, min(b, c))
#define max3(a, b, c) max(a, max(b, c))
typedef long long ll;
typedef unsigned long long ull;
using namespace std;
int main() {
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    ll n;
    cin >> n;
    ll mod = 1e9 + 7;
    if (n == 1) {
        cout << 0 << endl;
        return 0;
    }
    ll res = 1, temp1 = 1, temp2 = 1;
    for (int i = 0; i < n; i++) {
        res = res * 10 % mod;
        temp1 = temp1 * 9 % mod;
        temp2 = temp2 * 8 % mod;
    }
    res = res - 2 * temp1 + temp2;
    res = res % mod;
    cout << res << endl;
}