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<iostream>
#include<fstream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<deque>
#include<set>
#include<map>
#include<bitset>
#include<ctime>
#include<queue>
using namespace std;
#define int long long
#define pii pair <int, int>
#define XX first
#define YY second

// constants:
const int mn = 200005;
const int mod = 1000000007;
const long long inf = 4444444444444444444;
const int sminf = 1111111111;
const bool is_multitest = 0;
const bool is_interactive = 0;

// i/o methods:
const bool input_from_file = 0;
const bool output_to_file = 0;
#define filename ""
#define in_extension "inp"
#define out_extension "out"

// data preprocessing: (e.g.: divisor generating, prime sieve)
void preprocess()
{
  
}

// global variables:
int n;
int POW(int u, int v) {
  if (v == 0) return 1;
  int mid = POW(u, v/2);
  mid = (mid*mid)%mod;
  if (v&1) return (mid*u)%mod;
  else return mid;
}
// main solution goes here:
void execute(int test_number)
{
  cin>>n;
//   cout << POW(10, n) <<"\n";
  cout<<(POW(10, n) - POW(9, n) - POW(9, n) + POW(8, n) + 2*mod)%mod;
}
// REMEMBER TO CHOOSE TEST METHODS
// PLEASE REMOVE cout AND cerr DEBUG LINES BEFORE SUBMITTING PROBLEMS
// Solution by low_



















signed main()
{
#ifdef lowie
    if (!is_interactive)
    {
        freopen("test.inp", "r", stdin);
        freopen("test.out", "w", stdout);
    }
#else
    if (input_from_file) freopen(filename"."in_extension, "r", stdin);
    if (output_to_file) freopen(filename"."out_extension, "w", stdout);
#endif
    if (!is_interactive)
    {
        ios_base::sync_with_stdio(0);
        cin.tie(0);
        cout.tie(0);
    }

    preprocess();
    int ntest;
    if (is_multitest) cin >> ntest;
    else ntest = 1;

    for (int testno = 1; testno <= ntest; testno++)
    // use for instead of while to serve facebook hacker cup test format
    {
        execute(testno); // only start coding in this function, not in main
    }
}
// Template by low_
// Contact me via mail: ttuandung1803@gmail.com
// ...or codeforces: https://www.codeforces.com/profile/low_
// ...or linkedIn: https://www.linkedin.com/in/daniel-to-83045a19a/
// I use VS Code. Here's a JSON format for my template: https://pastebin.com/xH2yRdwx