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)

/*
digu_J - Digvijay Janartha
NIT Hamirpur - INDIA
*/

#include <bits/stdc++.h>
using namespace std;

const long long N = 1e6 + 5, MOD = 1e9 + 7;

long long dp[N][2][2];

void test() {
    int n;
    cin >> n;
    dp[0][0][0] = 1;
    for (int i = 1; i <= n; ++i) {
        dp[i][1][1] = (dp[i - 1][1][1] * 10 + dp[i - 1][1][0] + dp[i - 1][0][1]) % MOD;
        dp[i][1][0] = (dp[i - 1][1][0] * 9 + dp[i - 1][0][0]) % MOD;
        dp[i][0][1] = (dp[i - 1][0][1] * 9 + dp[i - 1][0][0]) % MOD;
        dp[i][0][0] = (dp[i - 1][0][0] * 8) % MOD;
    }
    cout << dp[n][1][1] << "\n";
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    #ifdef HOME
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    #endif
    int t = 1;
    // cin >> t;
    for (int i = 0; i < t; ++i) {
        test();
    }
    return 0;
}