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.Linq;
using CompLib.Util;
using System.Threading;
using CompLib.Collections.Generic;

public class Program
{
    int N, Q;
    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        Q = sc.NextInt();

        var row = new RangeUpdateQuery<int>(N, Math.Min, N - 1);
        var col = new RangeUpdateQuery<int>(N, Math.Min, N - 1);

        long ans = (long)(N - 2) * (N - 2);
        for (int q = 0; q < Q; q++)
        {
            int t = sc.NextInt();
            int x = sc.NextInt() - 1;

            if (t == 1)
            {
                int min = row[x];
                ans -= min - 1;
                col.Update(1, min, x);
            }
            else
            {
                int min = col[x];
                ans -= min - 1;
                row.Update(1, min, x);
            }
        }

        Console.WriteLine(ans);
    }

    public static void Main(string[] args) => new Program().Solve();
    // public static void Main(string[] args) => new Thread(new Program().Solve, 1 << 27).Start();
}


namespace CompLib.Collections.Generic
{
    using System;

    public class RangeUpdateQuery<T>
    {
        private readonly int N;
        private T[] _array;
        private readonly bool[] flag;

        private readonly T _identity;
        private readonly Func<T, T, T> _operation;

        /// <summary>
        /// 区間更新、点取得
        /// </summary>
        /// <param name="operation">更新用の演算</param>
        /// <param name="identity">(T, operation)の左単位元</param>
        public RangeUpdateQuery(int size, Func<T, T, T> operation, T identity)
        {
            N = 1;
            while (N < size) N *= 2;
            _identity = identity;
            _operation = operation;
            _array = new T[N * 2];
            for (int i = 1; i < N * 2; i++)
            {
                _array[i] = _identity;
            }

            flag = new bool[N * 2];
        }

        private void Eval(int k, int l, int r)
        {
            if (flag[k])
            {
                if (r - l > 1)
                {
                    _array[k * 2] = _operation(_array[k * 2], _array[k]);
                    flag[k * 2] = true;
                    _array[k * 2 + 1] = _operation(_array[k * 2 + 1], _array[k]);
                    flag[k * 2 + 1] = true;
                    _array[k] = _identity;
                }

                flag[k] = false;
            }
        }

        private void Update(int left, int right, int k, int l, int r, T item)
        {
            Eval(k, l, r);
            if (r <= left || right <= l)
            {
                return;
            }

            if (left <= l && r <= right)
            {
                _array[k] = _operation(_array[k], item);
                flag[k] = true;
                Eval(k, l, r);
                return;
            }

            Update(left, right, k * 2, l, (l + r) / 2, item);
            Update(left, right, k * 2 + 1, (l + r) / 2, r, item);
        }

        /// <summary> 
        /// [left,right)をoperation(A[i],item)に更新
        /// </summary>
        /// <param name="left"></param>
        /// <param name="right"></param>
        /// <param name="item"></param>
        public void Update(int left, int right, T item)
        {
            Update(left, right, 1, 0, N, item);
        }


        /// <summary>
        /// A[i]を取得 O(log N)
        /// </summary>
        /// <param name="i"></param>
        /// <returns></returns>
        public T Get(int i)
        {
            int l = 0;
            int r = N;
            int k = 1;
            while (r - l > 1)
            {
                Eval(k, l, r);
                int m = (l + r) / 2;
                if (i < m)
                {
                    r = m;
                    k = k * 2;
                }
                else
                {
                    l = m;
                    k = k * 2 + 1;
                }
            }

            return _array[k];
        }

        public T this[int i]
        {
            get { return Get(i); }
        }
    }
}


namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            if (_index >= _line.Length)
            {
                string s;
                do
                {
                    s = Console.ReadLine();
                } while (s.Length == 0);

                _line = s.Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public string ReadLine()
        {
            _index = _line.Length;
            return Console.ReadLine();
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            string s = Console.ReadLine();
            _line = s.Length == 0 ? new string[0] : s.Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}