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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.util.Locale.FilteringMode;

 
public class Main {
	static final long MOD1=1000000007;
	static final long MOD2=998244353;
	public static void main(String[] args) {
		PrintWriter out = new PrintWriter(System.out);
		InputReader sc=new InputReader(System.in);
		int N=sc.nextInt();
		int Q=sc.nextInt();
		LazysegTreemin xTreemin=new LazysegTreemin(N-1);
		LazysegTreemin yTreemin=new LazysegTreemin(N-1);
		long ans=0;
		long xmin=Integer.MAX_VALUE;
		long ymin=Integer.MAX_VALUE;
		xTreemin.update(0, N-1, (long)N-1, 0, 0, xTreemin.size);
		yTreemin.update(0, N-1, (long)N-1, 0, 0, xTreemin.size);
		for (int i = 0; i < Q; i++) {
			int c=sc.nextInt();
			int xx=sc.nextInt()-1;
			if (c==1) {
				long m=xTreemin.getmin(xx, xx+1, 0, 0, xTreemin.size);
				ans+=m-1;
				if (xmin>=xx) {
					yTreemin.update(0, (int)m+1, (long)xx, 0, 0, yTreemin.size);
					xmin=xx;
				}
			}else {
				long m=yTreemin.getmin(xx, xx+1, 0, 0, yTreemin.size);
				ans+=m-1;
				if (ymin>=xx) {
					xTreemin.update(0, (int)m+1, (long)xx, 0, 0, yTreemin.size);
					ymin=xx;
				}
			}
		}
		System.out.println((long)(N-2)*(long)(N-2)-ans);
	}
	static class LazysegTreemin{
		int size;
		long[] dat;
		long[] lazy;
		long INF=Long.MAX_VALUE/2;
		public LazysegTreemin(int n) {
			int n_=1;
			while (n_<n) {
				n_*=2;
			}
			size=n_;
			dat=new long[2*n_-1];
			lazy=new long[2*n_-1];
			Arrays.fill(dat, INF);
			Arrays.fill(lazy, INF);
		}
		void propagate(int k,int l,int r) {
			if (lazy[k]!=INF) {
				dat[k] = lazy[k];
				if(r - l > 1) {
		            lazy[2*k+1] = lazy[k];
		            lazy[2*k+2] = lazy[k];
		        }
		        lazy[k] = INF;
			}
		}
		void update(int a,int b,long x,int k,int l,int r) {//a<=x<b加算　add(...,0,0,seg.size)で呼ぶ
			this.propagate(k,l,r);
			if (a<=l&&r<=b) {
				lazy[k]=x;
				this.propagate(k,l,r);
			}
			else if (l<b&&a<r) {//交わっている場合
				this.update(a, b, x, k*2+1,l,(l+r)/2);
				this.update(a, b, x, k*2+2, (l+r)/2, r);
				dat[k] = Math.min(dat[2*k+1],dat[2*k+2]);
			}
		}
		long getmin(int a,int b,int k,int l,int r) {//kが節点番号,l rがその節点番号の範囲
			if (r<=a||b<=l) {
				return INF;
			}
			this.propagate(k, l, r);
			if (a<=l&&r<=b) {
				return dat[k];
			}
			else {
				long vl=this.getmin(a, b, k*2+1,l,(l+r)/2);
				long vr=this.getmin(a, b, k*2+2, (l+r)/2, r);
				return (Math.min(vl, vr));
			}
		}//getsum(x, y, 0, 0, size)で呼ぶ
	}
		static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
 
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}