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>

#define int long long

using namespace std;

const int MAXN = 1e6 + 100;

const int MOD = 1e9 + 7;

int dp[MAXN][4];

int32_t main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    int N;
    cin >> N;

    dp[0][0] = 1;

    for(int i = 1 ; i <= N ; i++)
    {
    	dp[i][0] = dp[i-1][0]*8;
    	dp[i][1] = dp[i-1][1]*9 + dp[i-1][0];
    	dp[i][2] = dp[i-1][2]*9 + dp[i-1][0];
    	dp[i][3] = dp[i-1][3]*10 + dp[i-1][1] + dp[i-1][2];

    	dp[i][0] %= MOD;
    	dp[i][1] %= MOD;
    	dp[i][2] %= MOD;
    	dp[i][3] %= MOD;
    }

    cout << dp[N][3] << '\n';

    return 0;
}