Problem:
Score : 600 points

Problem Statement

There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left.

Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it.
Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it.

Q queries are given. We ask you to process them in order.
There are two kinds of queries. Their input format and description are as follows:

1 x: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone.

2 x: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone.

How many black stones are there on the grid after processing all Q queries?

Constraints

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

0 \leq Q \leq \min(2N-4,2\times 10^5)

2 \leq x \leq N-1

Queries are pairwise distinct.

Input

Input is given from Standard Input in the following format:

N Q
Query_1
\vdots
Query_Q

Output

Print how many black stones there are on the grid after processing all Q queries.

Sample Input 1

5 5
1 3
2 3
1 4
2 2
1 2

Sample Output 1

1

After each query, the grid changes in the following way:

Sample Input 2

200000 0

Sample Output 2

39999200004

Sample Input 3

176527 15
1 81279
2 22308
2 133061
1 80744
2 44603
1 170938
2 139754
2 15220
1 172794
1 159290
2 156968
1 56426
2 77429
1 97459
2 71282

Sample Output 3

31159505795

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Diagnostics.Tracing;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Runtime.Intrinsics.X86;
using System.Security.Cryptography;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading;
using Extensions;
using DSA;
using static System.Math;
using static Extensions.MathExtension;
using static Extensions.ConsoleInputExtension;
using static Extensions.ConsoleOutputExtension;

class Solver
{
    public void Solve()
    {
        // checked
        {
            //Solve Code Here
            int n = Cin, q = Cin;
            long black = ((long) n - 2) * ((long) n - 2);
            var xCount = new SegTree<int>(Enumerable.Repeat(n - 2, n - 1).ToArray(), int.MaxValue, Min);
            var yCount = new SegTree<int>(Enumerable.Repeat(n - 2, n - 1).ToArray(), int.MaxValue, Min);
            for (int i = 0; i < q; i++)
            {
                int num = Cin;
                int x = Cin;
                if (num == 1)
                {
                    var count = yCount.Query(x - 2, n - 1);
                    black -= count;
                    if (xCount.Query(count, n - 1) > x - 2)
                        xCount.Update(count, x - 2);
                }
                else
                {
                    var count = xCount.Query(x - 2, n - 1);
                    black -= count;
                    if (yCount.Query(count, n - 1) > x - 2)
                        yCount.Update(count, x - 2);
                }
            }

            Coutln(black);
        }
    }
}

//Other Classes Here

#if !DEBUG
class EntryPoint
{
    static void Main(string[] args)
    {
        new Solver().Solve();
        Flush();
    }
}

#endif

namespace DSA
{
    public class PriorityQueue<T>
    {
        private readonly List<Tuple<int, T>> _list = new List<Tuple<int, T>>();

        public int Count => _list.Count;

        public void Push(T item, int priority)
        {
            _list.Add(Tuple.Create(priority, item));

            int itemIndex = Count - 1, parentIndex;
            while ((parentIndex = GetParentIndex(itemIndex)) != -1 &&
                   priority > _list[parentIndex].Item1)
            {
                Swap(itemIndex, parentIndex);
                itemIndex = parentIndex;
            }
        }

        private int GetParentIndex(int index)
        {
            if (index == 0) return -1;
            return ((index + 1) >> 1) - 1;
        }

        private Tuple<int, int> GetChildrenIndex(int index)
        {
            var item2 = (index + 1) << 1;
            var item1 = item2 - 1;
            return Tuple.Create(item1, item2);
        }

        public T Pop()
        {
            if (Count <= 0) throw new IndexOutOfRangeException();
            var item = _list[0].Item2;
            _list[0] = _list[Count - 1];
            _list.RemoveAt(Count - 1);

            int index = 0;
            Tuple<int, int> childrenIndex = GetChildrenIndex(index);
            while (childrenIndex.Item1 < Count || childrenIndex.Item2 < Count)
            {
                if (childrenIndex.Item2 >= Count || _list[childrenIndex.Item1].Item1 > _list[childrenIndex.Item2].Item1)
                {
                    if (_list[childrenIndex.Item1].Item1 <= _list[index].Item1) return item;

                    Swap(index, childrenIndex.Item1);
                    index = childrenIndex.Item1;
                }
                else
                {
                    if (_list[childrenIndex.Item2].Item1 <= _list[index].Item1) return item;
                    Swap(index, childrenIndex.Item2);
                    index = childrenIndex.Item2;
                }

                childrenIndex = GetChildrenIndex(index);
            }

            return item;
        }

        public T Peek()
        {
            return _list[0].Item2;
        }

        private void Swap(int index1, int index2)
        {
            var tmp = _list[index1];
            _list[index1] = _list[index2];
            _list[index2] = tmp;
        }
    }

    public class UnionFind
    {
        private readonly int[] _array;

        public UnionFind(int size)
        {
            _array = new int[size];
            for (int i = 0; i < size; i++)
            {
                _array[i] = i;
            }
        }

        public int GetRootNode(int n)
        {
            if (_array[n] == n) return n;
            return _array[n] = GetRootNode(_array[n]);
        }

        public void UnionGroup(int a, int b)
        {
            var rootA = GetRootNode(a);
            var rootB = GetRootNode(b);
            if (rootA == rootB) return;
            _array[rootA] = rootB;
        }

        public bool IsSameGroup(int a, int b) => GetRootNode(a) == GetRootNode(b);

        public bool IsRoot(int n) => _array[n] == n;
    }

    public delegate T SegTreeCombiner<T>(T item1, T item2);

    public class SegTree<T>
    {
        private readonly T _defaultItem;
        private readonly SegTreeCombiner<T> _func;
        private T[] List;
        private int size;

        public SegTree(T[] list, T defaultItem, SegTreeCombiner<T> func)
        {
            _defaultItem = defaultItem;
            _func = func;
            size = 1;
            while (size < list.Length) size <<= 1;
            List = new T[2 * size - 1];
            for (int i = 0; i < list.Length; i++) List[i + size - 1] = list[i];
            for (int i = list.Length; i < size; i++) List[i + size - 1] = defaultItem;
            for (int i = size - 1 - 1; i >= 0; i--)
            {
                List[i] = _func(List[2 * i + 1], List[2 * i + 2]);
            }
        }

        public T Get(int index)
        {
            return List[index];
        }

        public void Update(int index, T value)
        {
            index += size - 1;
            List[index] = value;
            while (index > 0)
            {
                index = (index - 1) >> 1;
                List[index] = _func(List[2 * index + 1], List[2 * index + 2]);
            }
        }

        public T Query(int a, int b)
        {
            return Query(a, b, 0, 0, size);
        }

        private T Query(int a, int b, int k, int l, int r)
        {
            if (r <= a || b <= l) return _defaultItem;
            if (a <= l && r <= b) return List[k];
            return _func(Query(a, b, k * 2 + 1, l, (l + r) >> 1), Query(a, b, k * 2 + 2, (l + r) >> 1, r));
        }
    }

    public static class BinarySearch
    {
        public delegate bool Terms<T>(T i);

        public static int UpperBound(int initLeft, int initRight, Terms<int> term)
        {
            int left = initLeft - 1, right = initRight;
            while (right - left > 1)
            {
                int mid = (left + right) >> 1;
                if (mid != initLeft - 1 && term(mid)) left = mid;
                else right = mid;
            }

            return left;
        }

        public static long UpperBound(long initLeft, long initRight, Terms<long> term)
        {
            long left = initLeft - 1, right = initRight;
            while (right - left > 1)
            {
                long mid = (left + right) >> 1;
                if (mid != initLeft - 1 && term(mid)) left = mid;
                else right = mid;
            }

            return left;
        }

        public static int LowerBound(int initLeft, int initRight, Terms<int> term)
        {
            int left = initLeft - 1, right = initRight;
            while (right - left > 1)
            {
                int mid = (left + right) >> 1;
                if (mid != initRight && term(mid)) right = mid;
                else left = mid;
            }

            return right;
        }

        public static long LowerBound(long initLeft, long initRight, Terms<long> term)
        {
            long left = initLeft - 1, right = initRight;
            while (right - left > 1)
            {
                long mid = (left + right) >> 1;
                if (term(mid)) right = mid;
                else left = mid;
            }

            return right;
        }
    }
}


struct ModInt
{
    public long Value { get; }
    public static long Mod { get; set; } = 1000000000L + 7;

    public ModInt(long l)
    {
        long value = l % Mod;
        while (value < 0) value += Mod;
        Value = value % Mod;
    }

    public static implicit operator long(ModInt m)
    {
        return m.Value;
    }

    public static implicit operator ModInt(long l)
    {
        return new ModInt(l);
    }

    public static ModInt operator +(ModInt a, ModInt b)
    {
        return new ModInt(a.Value + b.Value);
    }

    public static ModInt operator -(ModInt a, ModInt b)
    {
        return new ModInt(a.Value - b.Value);
    }

    public static ModInt operator *(ModInt a, ModInt b)
    {
        return new ModInt(a.Value * b.Value);
    }

    public static ModInt operator /(ModInt a, ModInt b)
    {
        return new ModInt(a * b.Inverse());
    }

    public override string ToString()
    {
        return Value.ToString();
    }
}

static class ModIntMath
{
    public static ModInt Pow(this ModInt a, ModInt b)
    {
        var pow = b.Value;
        var m = a;
        ModInt ans = new ModInt(1);
        while (pow != 0)
        {
            if ((pow & 1) == 1)
            {
                ans *= m;
            }

            pow >>= 1;
            m *= m;
        }

        return ans;
    }

    public static ModInt Inverse(this ModInt m)
    {
        return m.Pow((ModInt) (ModInt.Mod - 2));
    }
}


namespace Extensions
{
    public class ConsoleInputExtension
    {
        private static readonly ConsoleInputExtension _cin = new ConsoleInputExtension();

        public static ConsoleInputExtension Cin => _cin;

        private static readonly Queue<string> _inputQueue = new Queue<string>();

        private ConsoleInputExtension()
        {
        }

        public static implicit operator string(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0)
                Console.ReadLine().Split(' ')
                    .ForEach(val => _inputQueue.Enqueue(val));
            return _inputQueue.Dequeue();
        }

        public static implicit operator int(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0)
                Console.ReadLine().Split(' ')
                    .ForEach(val => _inputQueue.Enqueue(val));
            return int.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator long(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0)
                Console.ReadLine().Split(' ')
                    .ForEach(val => _inputQueue.Enqueue(val));
            return long.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator float(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0)
                Console.ReadLine().Split(' ')
                    .ForEach(val => _inputQueue.Enqueue(val));
            return float.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator double(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0)
                Console.ReadLine().Split(' ')
                    .ForEach(val => _inputQueue.Enqueue(val));
            return double.Parse(_inputQueue.Dequeue());
        }
    }

    public static class ConsoleOutputExtension
    {
        private static StringBuilder _builder = new StringBuilder();

        public static void Cout(object o)
        {
            _builder.Append(o);
        }


        public static void CoutF(object o)
        {
            _builder.Append(o);
            Flush();
        }

        public static void Coutln(object o)
        {
            _builder.Append(o);
            _builder.Append('\n');
        }

        public static void Coutln()
        {
            _builder.Append('\n');
        }

        public static void CoutlnF(object o)
        {
            _builder.Append(o);
            _builder.Append('\n');
            Flush();
        }

        public static void Flush()
        {
            Console.Write(_builder.ToString());
            _builder.Clear();
        }
    }

    public static class MathExtension
    {
        //最小公倍数
        public static int LCM(int num1, int num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        public static long LCM(long num1, long num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        //最大公約数
        public static int GCD(int num1, int num2)
        {
            int a = Math.Max(num1, num2);
            int b = Math.Min(num1, num2);
            if (b == 0) return a;
            int mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }

        public static long GCD(long num1, long num2)
        {
            long a = Math.Max(num1, num2);
            long b = Math.Min(num1, num2);
            if (b == 0) return a;
            long mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }
    }

    public static class EnumerableExtension
    {
        public delegate void Function<in T>(T val);

        public static void ForEach<T>(this IEnumerable<T> enumerable, Function<T> function)
        {
            foreach (var x in enumerable)
            {
                function(x);
            }
        }
    }
}