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.IO;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;

namespace FertiLib.Contest.C
{
	static class Program
	{
		public static void Solve(Scanner cin)
		{
			int n = cin.ReadInt();
			ModInt ans = ModInt.Pow(10, n);
			ans -= 2 * ModInt.Pow(9, n);
			ans += ModInt.Pow(8, n);
			Console.WriteLine(ans);
		}

		public static void Main(string[] args)
		{
			var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
			Console.SetOut(sw);
			var cin = new Scanner();
			Solve(cin);
			Console.Out.Flush();
		}

		public static void YESNO(bool condition) => Console.WriteLine(condition ? "YES" : "NO");
		public static void YesNo(bool condition) => Console.WriteLine(condition ? "Yes" : "No");
		public static void yesno(bool condition) => Console.WriteLine(condition ? "yes" : "no");

		public static bool Chmax<T>(ref T a, T b) where T : IComparable<T>
		{
			if (a.CompareTo(b) >= 0) return false;
			a = b;
			return true;
		}
		public static bool Chmin<T>(ref T a, T b) where T : IComparable<T>
		{
			if (a.CompareTo(b) <= 0) return false;
			a = b;
			return true;
		}
	}
	public struct ModInt : IComparable<ModInt>, IEquatable<ModInt>
	{
		public static long MOD = 1000000007;
		public static bool isModPrime { get; set; }

		private readonly long num;

		public ModInt(long n) { num = n; isModPrime = true; }

		public override string ToString() => num.ToString();

		public static ModInt operator +(ModInt l, ModInt r)
		{
			long x = l.num + r.num;
			if (x >= MOD) x -= MOD;
			return new ModInt(x);
		}
		public static ModInt operator -(ModInt l, ModInt r)
		{
			long x = l.num - r.num;
			if (x < 0) x += MOD;
			return new ModInt(x);
		}
		public static ModInt operator *(ModInt l, ModInt r) => new ModInt((l.num * r.num) % MOD);
		public static ModInt operator /(ModInt l, ModInt r) => l * r.Inverse();

		public static ModInt operator ++(ModInt x)
		{
			var tmp = x + new ModInt(1);
			return tmp;
		}
		public static ModInt operator --(ModInt x)
		{
			var tmp = x - new ModInt(1);
			return tmp;
		}

		public static bool operator >(ModInt l, ModInt r) => l.CompareTo(r) > 0;
		public static bool operator <(ModInt l, ModInt r) => l.CompareTo(r) < 0;
		public static bool operator >=(ModInt l, ModInt r) => l.CompareTo(r) >= 0;
		public static bool operator <=(ModInt l, ModInt r) => l.CompareTo(r) <= 0;
		public static bool operator ==(ModInt l, ModInt r) => l.Equals(r);
		public static bool operator !=(ModInt l, ModInt r) => !l.Equals(r);

		public static implicit operator long(ModInt x) => x.num;
		public static implicit operator ModInt(long n)
		{
			n %= MOD;
			if (n < 0) n += MOD;
			return new ModInt(n);
		}

		public ModInt Inverse() => Inverse(this, MOD);
		public static ModInt Inverse(ModInt x) => Inverse(x.num, MOD);
		public static long Inverse(long x, long m)
		{
			if (x % m == 0) throw new DivideByZeroException();
			long a = x, b = m, u = 1, v = 0;
			while (b > 0)
			{
				long t = a / b;

				a -= t * b;
				long p = a; a = b; b = p;   // swap(a, b);

				u -= t * v;
				p = u; u = v; v = p;        // swap(u, v);
			}
			u %= m;
			if (u < 0) u += m;
			return u;
		}

		public static ModInt Pow(long x, long n)
		{
			long now = 1;
			if (isModPrime) n %= MOD - 1;
			for (; n > 0; n /= 2, x = x * x % MOD)
			{
				if (n % 2 == 1) now = now * x % MOD;
			}
			return new ModInt(now);
		}

		public int CompareTo(ModInt x)
		{
			if (num == x.num) return 0;
			if (num > x.num) return 1;
			return -1;
		}

		public bool Equals(ModInt x) => num == x.num;

		public override bool Equals(object obj) => obj is ModInt m && num == m.num;

		public override int GetHashCode()
		{
			return HashCode.Combine(num);
		}

	}


	static class Extention
	{
		public static string Join<T>(this IEnumerable<T> x, string separator = "") => string.Join(separator, x);

		public static int UpperBound<T>(this IList<T> list, T value) => list.BinarySearch(value, true, 0, list.Count, Comparer<T>.Default);
		public static int LowerBound<T>(this IList<T> list, T value) => list.BinarySearch(value, false, 0, list.Count, Comparer<T>.Default);
		public static int BinarySearch<T>(this IList<T> list, T value, bool isUpperBound, int index, int length, Comparer<T> comparer)
		{
			var ng = index - 1;
			var ok = index + length;
			while (ok - ng > 1)
			{
				var mid = ng + (ok - ng) / 2;
				var res = comparer.Compare(list[mid], value);
				if (res < 0 || (isUpperBound && res == 0)) ng = mid;
				else ok = mid;
			}
			return ok;
		}
	}

	class Scanner
	{
		string[] s;
		int i;

		char[] separator = new char[] { ' ' };

		public Scanner()
		{
			s = new string[0];
			i = 0;
		}

		public string Read() => ReadString();

		public string ReadString()
		{
			if (i < s.Length) return s[i++];
			string st = Console.ReadLine();
			while (st == "") st = Console.ReadLine();
			s = st.Split(separator, StringSplitOptions.RemoveEmptyEntries);
			if (s.Length == 0) return ReadString();
			i = 0;
			return s[i++];
		}

		public string[] ReadStringArray(int N)
		{
			string[] Array = new string[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadString();
			}
			return Array;
		}

		public int ReadInt()
		{
			return int.Parse(ReadString());
		}

		public int[] ReadIntArray(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadInt() + add;
			}
			return Array;
		}

		public long ReadLong()
		{
			return long.Parse(ReadString());
		}

		public long[] ReadLongArray(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadLong() + add;
			}
			return Array;
		}

		public double ReadDouble()
		{
			return double.Parse(ReadString());
		}

		public double[] ReadDoubleArray(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadDouble() + add;
			}
			return Array;
		}

		public T1 ReadValue<T1>() => (T1)Convert.ChangeType(ReadString(), typeof(T1));

		public (T1, T2) ReadValue<T1, T2>()
		{
			var inputs = ReadStringArray(2);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			return (v1, v2);
		}

		public (T1, T2, T3) ReadValue<T1, T2, T3>()
		{
			var inputs = ReadStringArray(3);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
			return (v1, v2, v3);
		}

		public (T1, T2, T3, T4) ReadValue<T1, T2, T3, T4>()
		{
			var inputs = ReadStringArray(4);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
			var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
			return (v1, v2, v3, v4);
		}

		public (T1, T2, T3, T4, T5) ReadValue<T1, T2, T3, T4, T5>()
		{
			var inputs = ReadStringArray(5);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
			var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
			var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
			return (v1, v2, v3, v4, v5);
		}

		public (T1, T2, T3, T4, T5, T6) ReadValue<T1, T2, T3, T4, T5, T6>()
		{
			var inputs = ReadStringArray(6);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
			var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
			var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
			var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6));
			return (v1, v2, v3, v4, v5, v6);
		}

		public (T1, T2, T3, T4, T5, T6, T7) ReadValue<T1, T2, T3, T4, T5, T6, T7>()
		{
			var inputs = ReadStringArray(7);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
			var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
			var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
			var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6));
			var v7 = (T7)Convert.ChangeType(inputs[6], typeof(T7));
			return (v1, v2, v3, v4, v5, v6, v7);
		}

		public T1[] ReadValueArray<T1>(int N)
		{
			var v1 = new T1[N];
			for (int i = 0; i < N; i++)
			{
				v1[i] = ReadValue<T1>();
			}
			return v1;
		}

		public (T1[], T2[]) ReadValueArray<T1, T2>(int N)
		{
			var (v1, v2) = (new T1[N], new T2[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2) = ReadValue<T1, T2>();
				v1[i] = t1;
				v2[i] = t2;
			}
			return (v1, v2);
		}

		public (T1[], T2[], T3[]) ReadValueArray<T1, T2, T3>(int N)
		{
			var (v1, v2, v3) = (new T1[N], new T2[N], new T3[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3) = ReadValue<T1, T2, T3>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
			}
			return (v1, v2, v3);
		}

		public (T1[], T2[], T3[], T4[]) ReadValueArray<T1, T2, T3, T4>(int N)
		{
			var (v1, v2, v3, v4) = (new T1[N], new T2[N], new T3[N], new T4[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4) = ReadValue<T1, T2, T3, T4>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
			}
			return (v1, v2, v3, v4);
		}

		public (T1[], T2[], T3[], T4[], T5[]) ReadValueArray<T1, T2, T3, T4, T5>(int N)
		{
			var (v1, v2, v3, v4, v5) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4, t5) = ReadValue<T1, T2, T3, T4, T5>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
				v5[i] = t5;
			}
			return (v1, v2, v3, v4, v5);
		}

		public (T1[], T2[], T3[], T4[], T5[], T6[]) ReadValueArray<T1, T2, T3, T4, T5, T6>(int N)
		{
			var (v1, v2, v3, v4, v5, v6) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4, t5, t6) = ReadValue<T1, T2, T3, T4, T5, T6>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
				v5[i] = t5;
				v6[i] = t6;
			}
			return (v1, v2, v3, v4, v5, v6);
		}

		public (T1[], T2[], T3[], T4[], T5[], T6[], T7[]) ReadValueArray<T1, T2, T3, T4, T5, T6, T7>(int N)
		{
			var (v1, v2, v3, v4, v5, v6, v7) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N], new T7[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4, t5, t6, t7) = ReadValue<T1, T2, T3, T4, T5, T6, T7>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
				v5[i] = t5;
				v6[i] = t6;
				v7[i] = t7;
			}
			return (v1, v2, v3, v4, v5, v6, v7);
		}
	}
}