Problem:
Score : 400 points

Problem Statement

Given is a positive integer N.

Find the number of pairs (A, B) of positive integers not greater than N that satisfy the following condition:

When A and B are written in base ten without leading zeros, the last digit of A is equal to the first digit of B, and the first digit of A is equal to the last digit of B.

Constraints

1 \leq N \leq 2 \times 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

25

Sample Output 1

17

The following 17 pairs satisfy the condition: (1,1), (1,11), (2,2), (2,22), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (11,1), (11,11), (12,21), (21,12), (22,2), and (22,22).

Sample Input 2

1

Sample Output 2

1

Sample Input 3

100

Sample Output 3

108

Sample Input 4

2020

Sample Output 4

40812

Sample Input 5

200000

Sample Output 5

400000008

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using AtCoder.Algorithms;
using AtCoder.Collections;
using AtCoder.Extensions;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = Scanner.ReadInt();
            var array = new int[10, 10];

            for (int i = 1; i <= N; i++)
            {
                var str = i.ToString();
                array[str.First()-'0', str.Last() - '0']++;
            }

            int count=0;
            for (int i = 0; i <= 9; i++)
            {
                for (int j = 0; j <= 9; j++)
                {
                    count += array[i, j] * array[j, i];
                }
            }

            Console.WriteLine(count);
        }
    }
}

namespace AtCoder.Algorithms
{
}

namespace AtCoder.Collections
{
    public class Deque<T>
    {
        int dx;
        T[] buf;
        int mask;

        public int Count { get; private set; }
        public Deque() : this(8) { }
        public Deque(int capacity)
        {
            mask = capacity - 1;
            buf = new T[capacity];
        }
        public T this[int index]
        {
            get
            {
                return buf[(dx + index) & mask];
            }
            set
            {
                buf[(dx + index) & mask] = value;
            }
        }
        public void PushFront(T item)
        {
            if (Count == buf.Length) extend();
            dx = (dx + buf.Length - 1) & mask;
            buf[dx] = item;
            Count++;
        }
        public T PopFront()
        {
            var ret = buf[dx = (dx + 1) & mask];
            Count--;
            return ret;
        }
        public void PushBack(T item)
        {
            if (Count == buf.Length) extend();
            buf[(dx + Count++) & mask] = item;
        }
        public T PopBack()
        {
            var ret = buf[(dx + --Count) & mask];
            return ret;
        }
        public T Last()
        {
            return buf[(dx + Count - 1) & mask];
        }
        public T First()
        {
            return buf[dx];
        }
        void extend()
        {
            var nbuf = new T[buf.Length * 2];
            for (int i = 0; i < buf.Length; i++)
                nbuf[i] = buf[(dx + i) & mask];
            mask = mask * 2 + 1;
            dx = 0;
            buf = nbuf;
        }
        public void Clear() { Count = 0; }
        public bool Any() { return Count != 0; }
        public void Insert(int index, T item)
        {
            PushFront(item);
            for (int i = 0; i < index; i++)
                this[i] = this[i + 1];
            this[index] = item;
        }
        public T RemoveAt(int index)
        {
            var ret = this[index];
            for (int i = index; i > 0; i--)
                this[i] = this[i - 1];
            PopFront();
            return ret;
        }
        public T[] Items
        {
            get
            {

                var ret = new T[Count];
                for (int i = 0; i < Count; i++)
                    ret[i] = this[i];
                return ret;
            }
        }
    }
    public class PriorityQueue<T> : IEnumerable<T>
    {
        private readonly List<T> _data = new List<T>();
        private readonly IComparer<T> _comparer;
        private readonly bool _isDescending;

        public PriorityQueue(IComparer<T> comparer, bool isDescending = true)
        {
            _comparer = comparer;
            _isDescending = isDescending;
        }

        public PriorityQueue(Comparison<T> comparison, bool isDescending = true)
            : this(Comparer<T>.Create(comparison), isDescending)
        {
        }

        public PriorityQueue(bool isDescending = true)
            : this(Comparer<T>.Default, isDescending)
        {
        }

        public void Enqueue(T item)
        {
            _data.Add(item);
            var childIndex = _data.Count - 1;
            while (childIndex > 0)
            {
                var parentIndex = (childIndex - 1) / 2;
                if (Compare(_data[childIndex], _data[parentIndex]) >= 0)
                    break;
                Swap(childIndex, parentIndex);
                childIndex = parentIndex;
            }
        }

        public T Dequeue()
        {
            var lastIndex = _data.Count - 1;
            var firstItem = _data[0];
            _data[0] = _data[lastIndex];
            _data.RemoveAt(lastIndex--);
            var parentIndex = 0;
            while (true)
            {
                var childIndex = parentIndex * 2 + 1;
                if (childIndex > lastIndex)
                    break;
                var rightChild = childIndex + 1;
                if (rightChild <= lastIndex && Compare(_data[rightChild], _data[childIndex]) < 0)
                    childIndex = rightChild;
                if (Compare(_data[parentIndex], _data[childIndex]) <= 0)
                    break;
                Swap(parentIndex, childIndex);
                parentIndex = childIndex;
            }
            return firstItem;
        }

        public T Peek()
        {
            return _data[0];
        }

        private void Swap(int a, int b)
        {
            var tmp = _data[a];
            _data[a] = _data[b];
            _data[b] = tmp;
        }

        private int Compare(T a, T b)
        {
            return _isDescending ? _comparer.Compare(b, a) : _comparer.Compare(a, b);
        }

        public int Count => _data.Count;

        public IEnumerator<T> GetEnumerator()
        {
            return _data.GetEnumerator();
        }

        IEnumerator IEnumerable.GetEnumerator() => GetEnumerator();
    }
    public class PriorityQueue<TKey, TValue> : IEnumerable<TValue>
    {
        private readonly List<KeyValuePair<TKey, TValue>> _data = new List<KeyValuePair<TKey, TValue>>();
        private readonly bool _isDescending;
        private readonly Func<TValue, TKey> _keySelector;
        private readonly IComparer<TKey> _keyComparer;

        public PriorityQueue(Func<TValue, TKey> keySelector, bool isDescending = true)
            : this(keySelector, Comparer<TKey>.Default, isDescending)
        {
        }

        public PriorityQueue(Func<TValue, TKey> keySelector, IComparer<TKey> keyComparer, bool isDescending = true)
        {
            _keySelector = keySelector;
            _keyComparer = keyComparer;
            _isDescending = isDescending;
        }

        public void Enqueue(TValue item)
        {
            _data.Add(new KeyValuePair<TKey, TValue>(_keySelector(item), item));
            var childIndex = _data.Count - 1;
            while (childIndex > 0)
            {
                var parentIndex = (childIndex - 1) / 2;
                if (Compare(_data[childIndex].Key, _data[parentIndex].Key) >= 0)
                    break;
                Swap(childIndex, parentIndex);
                childIndex = parentIndex;
            }
        }

        public TValue Dequeue()
        {
            var lastIndex = _data.Count - 1;
            var firstItem = _data[0];
            _data[0] = _data[lastIndex];
            _data.RemoveAt(lastIndex--);
            var parentIndex = 0;
            while (true)
            {
                var childIndex = parentIndex * 2 + 1;
                if (childIndex > lastIndex)
                    break;
                var rightChild = childIndex + 1;
                if (rightChild <= lastIndex && Compare(_data[rightChild].Key, _data[childIndex].Key) < 0)
                    childIndex = rightChild;
                if (Compare(_data[parentIndex].Key, _data[childIndex].Key) <= 0)
                    break;
                Swap(parentIndex, childIndex);
                parentIndex = childIndex;
            }
            return firstItem.Value;
        }

        public TValue Peek()
        {
            return _data[0].Value;
        }

        private void Swap(int a, int b)
        {
            var tmp = _data[a];
            _data[a] = _data[b];
            _data[b] = tmp;
        }

        private int Compare(TKey a, TKey b)
        {
            return _isDescending ? _keyComparer.Compare(b, a) : _keyComparer.Compare(a, b);
        }

        public int Count => _data.Count;

        public IEnumerator<TValue> GetEnumerator()
        {
            return _data.Select(r => r.Value).GetEnumerator();
        }

        IEnumerator IEnumerable.GetEnumerator() => GetEnumerator();
    }
    /// <summary>
    /// Self-Balancing Binary Search Tree
    /// (using Randamized BST)
    /// </summary>
    public class SB_BinarySearchTree<T> where T : IComparable
    {
        public class Node
        {
            public T Value;
            public Node LChild;
            public Node RChild;
            public int Count;

            public Node(T v)
            {
                Value = v;
                Count = 1;
            }
        }
        static readonly Random _rnd = new Random();
        public static int Count(Node t)
        {
            return t == null ? 0 : t.Count;
        }
        static Node Update(Node t)
        {
            t.Count = Count(t.LChild) + Count(t.RChild) + 1;
            return t;
        }
        public static Node Merge(Node l, Node r)
        {
            if (l == null || r == null) return l == null ? r : l;

            if (Count(l) / (double)(Count(l) + Count(r)) > _rnd.NextDouble())
            {
                l.RChild = Merge(l.RChild, r);
                return Update(l);
            }
            else
            {
                r.LChild = Merge(l, r.LChild);
                return Update(r);
            }
        }
        /// <summary>
        /// split as [0, k), [k, n)
        /// </summary>
        public static Tuple<Node, Node> Split(Node t, int k)
        {
            if (t == null) return new Tuple<Node, Node>(null, null);
            if (k <= Count(t.LChild))
            {
                var s = Split(t.LChild, k);
                t.LChild = s.Item2;
                return new Tuple<Node, Node>(s.Item1, Update(t));
            }
            else
            {
                var s = Split(t.RChild, k - Count(t.LChild) - 1);
                t.RChild = s.Item1;
                return new Tuple<Node, Node>(Update(t), s.Item2);
            }
        }
        public static Node Remove(Node t, T v)
        {
            if (Find(t, v) == null) return t;
            return RemoveAt(t, LowerBound(t, v));
        }
        public static Node RemoveAt(Node t, int k)
        {
            var s = Split(t, k);
            var s2 = Split(s.Item2, 1);
            return Merge(s.Item1, s2.Item2);
        }
        public static bool Contains(Node t, T v)
        {
            return Find(t, v) != null;
        }
        public static Node Find(Node t, T v)
        {
            while (t != null)
            {
                var cmp = t.Value.CompareTo(v);
                if (cmp > 0) t = t.LChild;
                else if (cmp < 0) t = t.RChild;
                else break;
            }
            return t;
        }
        public static Node FindByIndex(Node t, int idx)
        {
            if (t == null) return null;

            var currentIdx = Count(t) - Count(t.RChild) - 1;
            while (t != null)
            {
                if (currentIdx == idx) return t;
                if (currentIdx > idx)
                {
                    t = t.LChild;
                    currentIdx -= (Count(t == null ? null : t.RChild) + 1);
                }
                else
                {
                    t = t.RChild;
                    currentIdx += (Count(t == null ? null : t.LChild) + 1);
                }
            }

            return null;
        }
        public static int UpperBound(Node t, T v)
        {
            var torg = t;
            if (t == null)
                return -1;

            var ret = int.MaxValue;
            var idx = Count(t) - Count(t.RChild) - 1;
            while (t != null)
            {
                var cmp = t.Value.CompareTo(v);

                if (cmp > 0)
                {
                    ret = Math.Min(ret, idx);
                    t = t.LChild;
                    idx -= (Count(t == null ? null : t.RChild) + 1);
                }
                else if (cmp <= 0)
                {
                    t = t.RChild;
                    idx += (Count(t == null ? null : t.LChild) + 1);
                }
            }
            return ret == int.MaxValue ? Count(torg) : ret;
        }
        public static int LowerBound(Node t, T v)
        {
            var torg = t;
            if (t == null) return -1;

            var idx = Count(t) - Count(t.RChild) - 1;
            var ret = int.MaxValue;
            while (t != null)
            {
                var cmp = t.Value.CompareTo(v);
                if (cmp >= 0)
                {
                    if (cmp == 0) ret = Math.Min(ret, idx);
                    t = t.LChild;
                    if (t == null) ret = Math.Min(ret, idx);
                    idx -= t == null ? 0 : (Count(t.RChild) + 1);
                }
                else if (cmp < 0)
                {
                    t = t.RChild;
                    idx += (Count(t == null ? null : t.LChild) + 1);
                    if (t == null) return idx;
                }
            }
            return ret == int.MaxValue ? Count(torg) : ret;
        }
        public static Node Insert(Node t, T v)
        {
            var ub = LowerBound(t, v);
            return InsertByIdx(t, ub, v);
        }
        static Node InsertByIdx(Node t, int k, T v)
        {
            var s = Split(t, k);
            return Merge(Merge(s.Item1, new Node(v)), s.Item2);
        }
        public static IEnumerable<T> Enumerate(Node t)
        {
            var ret = new List<T>();
            Enumerate(t, ret);
            return ret;
        }
        static void Enumerate(Node t, List<T> ret)
        {
            if (t == null) return;
            Enumerate(t.LChild, ret);
            ret.Add(t.Value);
            Enumerate(t.RChild, ret);
        }
    }
    public class Set<T> where T : IComparable
    {
        protected SB_BinarySearchTree<T>.Node _root;

        public T this[int idx] { get { return ElementAt(idx); } }

        public int Count()
        {
            return SB_BinarySearchTree<T>.Count(_root);
        }

        public virtual void Insert(T v)
        {
            if (_root == null) _root = new SB_BinarySearchTree<T>.Node(v);
            else
            {
                if (SB_BinarySearchTree<T>.Find(_root, v) != null) return;
                _root = SB_BinarySearchTree<T>.Insert(_root, v);
            }
        }

        public void Clear()
        {
            _root = null;
        }

        public void Remove(T v)
        {
            _root = SB_BinarySearchTree<T>.Remove(_root, v);
        }

        public bool Contains(T v)
        {
            return SB_BinarySearchTree<T>.Contains(_root, v);
        }

        public T ElementAt(int k)
        {
            var node = SB_BinarySearchTree<T>.FindByIndex(_root, k);
            if (node == null) throw new IndexOutOfRangeException();
            return node.Value;
        }

        public int Count(T v)
        {
            return SB_BinarySearchTree<T>.UpperBound(_root, v) - SB_BinarySearchTree<T>.LowerBound(_root, v);
        }

        public int LowerBound(T v)
        {
            return SB_BinarySearchTree<T>.LowerBound(_root, v);
        }

        public int UpperBound(T v)
        {
            return SB_BinarySearchTree<T>.UpperBound(_root, v);
        }

        public Tuple<int, int> EqualRange(T v)
        {
            if (!Contains(v)) return new Tuple<int, int>(-1, -1);
            return new Tuple<int, int>(SB_BinarySearchTree<T>.LowerBound(_root, v), SB_BinarySearchTree<T>.UpperBound(_root, v) - 1);
        }

        public List<T> ToList()
        {
            return new List<T>(SB_BinarySearchTree<T>.Enumerate(_root));
        }
    }
    public class MultiSet<T> : Set<T> where T : IComparable
    {
        public override void Insert(T v)
        {
            if (_root == null) _root = new SB_BinarySearchTree<T>.Node(v);
            else _root = SB_BinarySearchTree<T>.Insert(_root, v);
        }
    }
    public class UnionFind<T>
    {
        private Dictionary<T, T> _parent = new Dictionary<T, T>();
        private Dictionary<T, int> _size = new Dictionary<T, int>();

        public void Unite(T x, T y)
        {
            x = Root(x);
            y = Root(y);

            if (IsEqual(x, y)) return;

            var sx = Size(x);
            var sy = Size(y);
            if (sx < sy)
            {
                var t = x;
                x = y;
                y = t;
            }
            _size[x] += _size[y];
            _size.Remove(y);
            _parent[y] = x;
        }
        public int Size(T x)
        {
            var p = Root(x);

            int s;
            if (_size.TryGetValue(p, out s))
            {
                return s;
            }

            return _size[x] = 1;
        }
        public bool IsSameGroup(T x, T y)
        {
            return IsEqual(Root(x), Root(y));
        }
        public bool IsRoot(T x)
        {
            return IsEqual(Root(x), x);
        }
        private T Root(T x)
        {
            T r;
            if (_parent.TryGetValue(x, out r))
            {
                return _parent[x] = Root(r);
            }

            return x;
        }
        private bool IsEqual(T x, T y)
        {
            return EqualityComparer<T>.Default.Equals(x, y);
        }
    }
}

namespace AtCoder.Mathematics
{
    public class MathEx
    {
        /// <summary>
        /// 最小公倍数
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        static long Lcm(long a, long b)
        {
            return a / Gcd(a, b) * b;
        }
        /// <summary>
        /// 最大公約数
        /// </summary>
        /// <param name="m"></param>
        /// <param name="n"></param>
        /// <returns></returns>
        static long Gcd(long m, long n)
        {
            if (n == 0) return m;
            return Gcd(n, m % n);
        }
    }
    public struct ModInt
    {
        public const long Mod = (int)1e9 + 7;
        public long num;
        public ModInt(long n) { num = n; }
        public override string ToString() { return num.ToString(); }
        public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; }
        public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; }
        public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); }
        public static ModInt operator /(ModInt l, ModInt r) { return l * Pow(r, Mod - 2); }
        public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); }
        public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); }
        public static ModInt Pow(long v, long k)
        {
            long ret = 1;
            for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
                if ((k & 1) == 1) ret = ret * v % Mod;
            return new ModInt(ret);
        }
        public static ModInt Combination(long n, long r)
        {
            ModInt ans = 1;
            for (int i = 0; i < r; i++)
            {
                ans *= n - i;
            }
            for (int i = 1; i <= r; i++)
            {
                ans /= i;
            }
            return ans;
        }
        public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); }
    }
}

namespace AtCoder.Extensions
{
    public static class Extension
    {
        static int BinarySearch<T>(IList<T> source, T value, IComparer<T> comparer, bool isLowerBound)
        {
            return BinarySearch(source, 0, source.Count - 1, value, comparer, isLowerBound);
        }
        static int BinarySearch<T>(IList<T> source, int start, int end, T value, IComparer<T> comparer, bool isLowerBound)
        {
            while (start <= end)
            {
                var mid = (start + end) / 2;
                var result = comparer.Compare(source[mid], value);
                if (result < 0 || (result == 0 && !isLowerBound)) start = mid + 1;
                else end = mid - 1;
            }
            return start;
        }
        public static int LowerBound<T>(this IList<T> source, T value, Comparison<T> f) => BinarySearch(source, value, Comparer<T>.Create(f), true);
        public static int LowerBound<T>(this IList<T> source, int start, T value, Comparison<T> f) => BinarySearch(source, start, source.Count - 1, value, Comparer<T>.Create(f), true);
        public static int LowerBound<T>(this IList<T> source, int start, int end, T value, Comparison<T> f) => BinarySearch(source, start, end, value, Comparer<T>.Create(f), true);
        public static int LowerBound<T>(this IList<T> source, T value) => BinarySearch(source, value, Comparer<T>.Default, true);
        public static int LowerBound<T>(this IList<T> source, int start, T value) => BinarySearch(source, start, source.Count - 1, value, Comparer<T>.Default, true);
        public static int LowerBound<T>(this IList<T> source, int start, int end, T value) => BinarySearch(source, start, end, value, Comparer<T>.Default, true);
        public static int UpperBound<T>(this IList<T> source, T value, Comparison<T> cmp) => BinarySearch(source, value, Comparer<T>.Create(cmp), false);
        public static int UpperBound<T>(this IList<T> source, int start, T value, Comparison<T> cmp) => BinarySearch(source, start, source.Count - 1, value, Comparer<T>.Create(cmp), false);
        public static int UpperBound<T>(this IList<T> source, int start, int end, T value, Comparison<T> cmp) => BinarySearch(source, start, end, value, Comparer<T>.Create(cmp), false);
        public static int UpperBound<T>(this IList<T> source, T value) => BinarySearch(source, value, Comparer<T>.Default, false);
        public static int UpperBound<T>(this IList<T> source, int start, T value) => BinarySearch(source, start, source.Count - 1, value, Comparer<T>.Default, false);
        public static int UpperBound<T>(this IList<T> source, int start, int end, T value) => BinarySearch(source, start, end, value, Comparer<T>.Default, false);
        public static PriorityQueue<T> AsPriorityQueue<T>(this IEnumerable<T> source, bool isDescending = true)
        {
            var queue = new PriorityQueue<T>(isDescending);
            foreach (var item in source)
            {
                queue.Enqueue(item);
            }

            return queue;
        }
        public static PriorityQueue<TKey, TSource> AsPriorityQueue<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector, bool isDescending = true)
        {
            var queue = new PriorityQueue<TKey, TSource>(keySelector, isDescending);
            foreach (var item in source)
            {
                queue.Enqueue(item);
            }

            return queue;
        }
        public static bool ChangeMin<T>(this IList<T> source, int index, T value)
            where T : IComparable
        {
            var a = source[index];
            if (a.CompareTo(value) > 0)
            {
                source[index] = value;
                return true;
            }
            return false;
        }
        public static bool ChangeMax<T>(this IList<T> source, int index, T value)
            where T : IComparable
        {
            var a = source[index];
            if (a.CompareTo(value) < 0)
            {
                source[index] = value;
                return true;
            }
            return false;
        }
    }
    public static class Scanner
    {
        public static string ReadString() => Console.ReadLine();
        public static int ReadInt() => int.Parse(Console.ReadLine());
        public static long ReadLong() => long.Parse(Console.ReadLine());
        public static double ReadDouble() => double.Parse(Console.ReadLine());
        public static string[] ReadStringArray() => Console.ReadLine().Split().ToArray();
        public static string[] ReadStringArray(int n) => Enumerable.Range(0, n).Select(_ => Console.ReadLine()).ToArray();
        public static int[] ReadIntArray() => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static int[] ReadIntArray(int n) => Enumerable.Range(0, n).Select(_ => ReadInt()).ToArray();
        public static long[] ReadLongArray() => Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        public static long[] ReadLongArray(int n) => Enumerable.Range(0, n).Select(_ => ReadLong()).ToArray();
        public static double[] ReadDoubleArray() => Console.ReadLine().Split().Select(double.Parse).ToArray();
        public static double[] ReadDoubleArray(int n) => Enumerable.Range(0, n).Select(_ => ReadDouble()).ToArray();
    }
}