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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using static System.Math;

namespace CSharpSpiral {
	class Program {
		public static void Main(string[] args) {
			var sw = new StreamWriter(Console.OpenStandardOutput()) {
				AutoFlush =
#if DEBUG
			true
#else
			false
#endif
			};
			Console.SetOut(sw);
			new Program().Solve(new ConsoleInput(
#if DEBUG
			new StreamReader("../../../inputData.txt")
#else
			Console.In
#endif
			, ' '));
			Console.Out.Flush();
		}

		public void Solve(ConsoleInput cin) {
			var F = new QuotientRing();
			var N = cin.ReadLong;
			Console.WriteLine(F.Calculate(10L, N, '^', 8L, N, '^', '+', 9L, N, '^', 2L, '*', '-'));
		}
	}

	class QuotientRing {
		public readonly long modulo;
		public QuotientRing(int mModulo = 1000 * 1000 * 1000 + 7) {
			modulo = mModulo;
		}
		private long[] factorialTable = { 1 };
		protected int factorialTableLastIndex { get { return factorialTable.Length - 1; } }
		public long mod(long x) => x < 0 ? x % modulo + modulo : x % modulo;
		public long Add(long a, long b) => mod(a + b);
		public long Sub(long a, long b) => mod(a - b);
		public long Mul(long a, long b) => mod(a * b);
		public long Pow(long a, long n) {
			if(n == 0) return 1;
			var R = 1L;
			n = n < 0 ? n % (modulo - 1) + (modulo - 1) : n % (modulo - 1);
			for(; n > 0; a = Mul(a, a), n >>= 1) {
				if((n & 1) != 0) R = Mul(R, a);
			}
			return R;
		}
		private void ExpandFactorialTable(int N) {
			var k = factorialTableLastIndex;
			Array.Resize(ref factorialTable, N + 1);
			for(int i = k + 1; i <= N; i++) {
				if(i == 0) { factorialTable[i] = 1; continue; }
				factorialTable[i] = Mul(factorialTable[i - 1], i);
			}
		}
		public long Factorial(int n) {
			if(n > factorialTableLastIndex)
				ExpandFactorialTable(n);
			return factorialTable[n];
		}
		public virtual long Permutation(int n, int k) {
			if(k < 0 || k > n) return 0;
			var Res = 1L;
			for(int i = 0; i < k; i++)
				Res = Mul(Res, n - i);
			return Res;
		}
		public virtual long Calculate(params object[] RPN) {
			var S = new Stack<long>();
			foreach(var token in RPN) {
				var type = token.GetType();
				if(type == typeof(int) || type == typeof(long)) {
					S.Push((long)token);
				} else if(type == typeof(char)) {
					long v1 = 0L, v2 = 0L;
					v2 = S.Pop();
					HashSet<char> unaries = new HashSet<char>() { '!' };
					if(!unaries.Contains((char)token))
						v1 = S.Pop();
					var res = ((char)token) switch
					{
						'+' => Add(v1, v2),
						'-' => Sub(v1, v2),
						'*' => Mul(v1, v2),
						'^' => Pow(v1, v2),
						'!' => Factorial((int)v2),
						_ => throw new InvalidOperationException(),
					};
					S.Push(res);
				} else throw new InvalidOperationException();
			}
			return S.Peek();
		}
	}

	static class ExtendClass {
		public static string Join<T>(this IEnumerable<T> X, string separator = " ")
			=> string.Join(separator, X);
	}
	class ConsoleInput {
		private readonly TextReader _stream;
		private readonly char _separator = ' ';
		private readonly Queue<string> inputStream;
		public ConsoleInput(TextReader stream, char separator = ' ') {
			this._separator = separator;
			this._stream = stream;
			inputStream = new Queue<string>();
		}
		public string Read {
			get {
				if(inputStream.Count != 0) return inputStream.Dequeue();
				string[] tmp = _stream.ReadLine().Split(_separator);
				for(int i = 0; i < tmp.Length; ++i)
					inputStream.Enqueue(tmp[i]);
				return inputStream.Dequeue();
			}
		}
		public string ReadLine { get { return _stream.ReadLine(); } }
		public int ReadInt { get { return int.Parse(Read); } }
		public long ReadLong { get { return long.Parse(Read); } }
		public double ReadDouble { get { return double.Parse(Read); } }
		public string[] ReadStrArray(long N) {
			var ret = new string[N];
			for(long i = 0; i < N; ++i)
				ret[i] = Read;
			return ret;
		}
		public int[] ReadIntArray(long N) { var ret = new int[N]; for(long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
		public long[] ReadLongArray(long N) { var ret = new long[N]; for(long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
		public double[] ReadDoubleArray(long N) { var ret = new double[N]; for(long i = 0; i < N; ++i) ret[i] = ReadDouble; return ret; }
		public bool isEOF {
			get { return _stream.Peek() == -1; }
		}
	}

}