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.Linq;
using System.Collections;
using System.Collections.Generic;

namespace ABC178
{
    using static Ex;
    public class Solve
    {
        public static void Main(string[] args)
        {
            new ABC_C();
        }
    }
    public class ABC_A
    {
        public ABC_A()
        {
            var x = ReadInt;
            if (x == 0) 1.Cw();
            else 0.Cw();
        }
    }
    public class ABC_B
    {
        public ABC_B()
        {
            var (a, b, c, d) = ReadLongArray().ToTpl4();
            long max = long.MinValue;
            Maxs(ref max, a * c);
            Maxs(ref max, b * c);
            Maxs(ref max, a * d);
            Maxs(ref max, b * d);
            max.Cw();
        }
    }
    public class ABC_C
    {
        public ABC_C()
        {
            long n = ReadLong;
            (Pow(10, n) - Pow(9, n) - Pow(9, n) + Pow(8, n)).Data.Cw();
        }
    }

    public static class Ex
    {
        public static void Cw(this object s) { Console.WriteLine(s); }



        public static bool Mins<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) > 0) { a = b; return true; } return false; }
        public static bool Maxs<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
        public static void Swap<T>(ref T a, ref T b) { var t = b; b = a; a = t; }
        public static void Swap<T>(List<T> list, int i, int j) { T tmp = list[j]; list[j] = list[i]; list[i] = tmp; }

        public static long Lcm(int x, int y) { return x / Gcd(x, y) * y; }
        public static long Gcd(long m, long n) { if (n == 0) return m; return Gcd(n, m % n); }
        public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.Ordinal); return s.ToList(); }
        public static void yesno(this bool b) { (b ? "yes" : "no").Cw(); }
        public static void YesNo(this bool b) { (b ? "Yes" : "No").Cw(); }
        public static void YESNO(this bool b) { (b ? "YES" : "NO").Cw(); }

        public static string Read { get { return Console.ReadLine().Trim(); } }
        public static int ReadInt { get { return int.Parse(Read); } }
        public static long ReadLong { get { return long.Parse(Read); } }
        public static double ReadDouble { get { return double.Parse(Read); } }
        public static string[] ReadArray() { return Read.Split(' '); }
        public static int[] ReadIntArray() { return Read.Split(' ').Select(int.Parse).ToArray(); }
        public static long[] ReadLongArray() { return Read.Split(' ').Select(long.Parse).ToArray(); }
        public static string[] ReadArray(long N) { var v = new string[N]; for (long i = 0; i < N; ++i) v[i] = Read; return v; }
        public static int[] ReadIntArray(long N) { var v = new int[N]; for (long i = 0; i < N; ++i) v[i] = ReadInt; return v; }
        public static long[] ReadLongArray(long N) { var v = new long[N]; for (long i = 0; i < N; ++i) v[i] = ReadLong; return v; }

        public static (T, T) ToTpl2<T>(this T[] v) { return (v[0], v[1]); }
        public static (T, T, T) ToTpl3<T>(this T[] v) { return (v[0], v[1], v[2]); }
        public static (T, T, T, T) ToTpl4<T>(this T[] v) { return (v[0], v[1], v[2], v[3]); }
        public static (T, T, T, T, T) ToTpl5<T>(this T[] v) { return (v[0], v[1], v[2], v[3], v[4]); }

        /// <summary>
        /// 与えられた 2 つの数値からべき剰余を計算します．
        /// </summary>
        /// <param name="v">べき乗の底</param>
        /// <param name="k">べき指数</param>
        /// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
        public static ModInt Power(ModInt v, long k) { return Pow(v.Data, k); }

        /// <summary>
        /// 与えられた 2 つの数値からべき剰余を計算します．
        /// </summary>
        /// <param name="v">べき乗の底</param>
        /// <param name="k">べき指数</param>
        /// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
        public static ModInt Pow(long v, long k)
        {
            long ret = 1;
            for (k %= ModInt.Mod - 1; k > 0; k >>= 1, v = v * v % ModInt.Mod)
                if ((k & 1) == 1) ret = ret * v % ModInt.Mod;
            return new ModInt(ret);
        }
        /// <summary>
        /// 与えられた数の逆元を計算します．
        /// </summary>
        /// <param name="v">逆元を取る対象となる数</param>
        /// <returns>逆元となるような値</returns>
        /// <remarks>法が素数であることを仮定して，フェルマーの小定理に従って逆元を O(log N) で計算します．</remarks>
        public static ModInt Inverse(ModInt v) { return Pow(v, ModInt.Mod - 2); }

        public struct ModInt
        {
            public const int Mod = (int)1e9 + 7;
            const long POSITIVIZER = ((long)Mod) << 31;
            public long Data;
            public ModInt(long data) { if ((Data = data % Mod) < 0) Data += Mod; }
            public static implicit operator long(ModInt modInt) => modInt.Data;
            public static implicit operator ModInt(long val) => new ModInt(val);
            public static ModInt operator +(ModInt a, int b) => new ModInt() { Data = (a.Data + b + POSITIVIZER) % Mod };
            public static ModInt operator +(ModInt a, long b) => new ModInt(a.Data + b);
            public static ModInt operator +(ModInt a, ModInt b) { long res = a.Data + b.Data; return new ModInt() { Data = res >= Mod ? res - Mod : res }; }
            public static ModInt operator -(ModInt a, int b) => new ModInt() { Data = (a.Data - b + POSITIVIZER) % Mod };
            public static ModInt operator -(ModInt a, long b) => new ModInt(a.Data - b);
            public static ModInt operator -(ModInt a, ModInt b) { long res = a.Data - b.Data; return new ModInt() { Data = res < 0 ? res + Mod : res }; }
            public static ModInt operator *(ModInt a, int b) => new ModInt(a.Data * b);
            public static ModInt operator *(ModInt a, long b) => a * new ModInt(b);
            public static ModInt operator *(ModInt a, ModInt b) => new ModInt() { Data = a.Data * b.Data % Mod };
            public static ModInt operator /(ModInt a, ModInt b) => new ModInt() { Data = a.Data * GetInverse(b) % Mod };
            public static bool operator ==(ModInt a, ModInt b) => a.Data == b.Data;
            public static bool operator !=(ModInt a, ModInt b) => a.Data != b.Data;
            public override string ToString() => Data.ToString();
            public override bool Equals(object obj) => (ModInt)obj == this;
            public override int GetHashCode() => (int)Data;
            static long GetInverse(long a)
            {
                long div, p = Mod, x1 = 1, y1 = 0, x2 = 0, y2 = 1;
                while (true)
                {
                    if (p == 1) return x2 + Mod; div = a / p; x1 -= x2 * div; y1 -= y2 * div; a %= p;
                    if (a == 1) return x1 + Mod; div = p / a; x2 -= x1 * div; y2 -= y1 * div; p %= a;
                }
            }
        }
    }
}