Problem: 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.

Examples

Input

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


Output

1


Input

200000 0


Output

39999200004


Input

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


Output

31159505795

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import static java.lang.Math.*;

public class Main {
    public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int n = sc.nextInt();
		int q = sc.nextInt();
		int I = n;
		int J = n;
		long black = (long)(n-2)*(n-2);
		BIT IBit = new BIT(n, 2);
		IBit.add(0, n-1, n-2);
		BIT JBit = new BIT(n, 2);
		JBit.add(0, n-1, n-2);
		for(int i = 0; i < q; i++){
		    int a = sc.nextInt();
		    int index = sc.nextInt()-1;
		    if(a == 1){
		        long cntI = IBit.get(index);
		        black -= cntI;
		        long cntJ = JBit.get((int)cntI);
		        if(index-1 < cntJ){
		            JBit.add(0, (int)cntI, (index-1) - cntJ);
		        }
		    }else{
		        long cntJ = JBit.get(index);
		        black -= cntJ;
		        long cntI = IBit.get((int)cntJ);
		        if(index-1 < cntI){
		            IBit.add(0, (int)cntJ, (index-1) - cntI);
		        }
		    }
		}
		
		// 計算
		long result = black;
		
		// 出力
		System.out.println(result);
		
	}
	
	public static class Scanner {
		private BufferedReader br; private StringTokenizer tok;
		public Scanner(InputStream is) throws IOException { br = new BufferedReader(new InputStreamReader(is));}
		private void getLine() throws IOException { while(!hasNext()) tok = new StringTokenizer(br.readLine());}
		private boolean hasNext() { return tok != null && tok.hasMoreTokens();}
		public String next() throws IOException { getLine(); return tok.nextToken();}
		public int nextInt() throws IOException { return Integer.parseInt(next());}
		public long nextLong() throws IOException { return Long.parseLong(next());}
		public double nextDouble() throws IOException { return Double.parseDouble(next());}
	}

}

class BIT {
	int n;
	long[] array;
	int mode = 1;
	
	public BIT(int n){
		this.n = n;
		this.array = new long[n+1];
	}
	
	public BIT(int n, int mode){
		this.n = n;
		this.array = new long[n+1];
		this.mode = mode;
	}
	
	public BIT(int[] a){
		this.n = a.length;
		this.array = new long[n+1];
		init(a);
	}
	public BIT(long[] a){
		this.n = a.length;
		this.array = new long[n+1];
		init(a);
	}
	
	public BIT(int[] a, int mode){
		this.n = a.length;
		this.array = new long[n+1];
		this.mode = mode;
		init(a);
	}
	public BIT(long[] a, int mode){
		this.n = a.length;
		this.array = new long[n+1];
		this.mode = mode;
		init(a);
	}
	
	public void init(int[] a){
		for(int i = 0; i < n; i++){
			add(i, a[i]);
		}
	}
	public void init(long[] a){
		for(int i = 0; i < n; i++){
			add(i, a[i]);
		}
	}

	public void add(int i, long a){
		switch(mode){
			case 1:
				for(i++; i < array.length; i += i&-i){
					array[i] += a;
				}
				break;
				
			case 2:
				add(i, i, a);
				break;
				
			default:
		}
	}
	
	public void add(int from, int to, long a){ // mode 2 only
		switch(mode){
			case 1:
				break;
				
			case 2:
				int i = from;
				for(i++; i < array.length; i += i&-i){
					array[i] += a;
				}
				i = to + 1;
				for(i++; i < array.length; i += i&-i){
					array[i] -= a;
				}
				break;
				
			default:
		}
	}
	
	public long get(int i){
		switch(mode){
			case 1:
				return getSum(i, i);
			case 2:
				return getSum(i);
			default:
				return getSum(i, i);
		}
	}
	
	public long getSum(int i){
		long r = 0;
		for(i++; i > 0; i -= i&-i){
			r += array[i];
		}
		return r;
	}
	
	public long getSum(int from, int to){ // mode 1 only
		return getSum(to) - getSum(from - 1);
	}
	
	public String toString(){
		StringBuilder sb = new StringBuilder();
		sb.append("[");
		for(int i = 0; i < n; i++){
			sb.append(get(i));
			if(i != n-1) sb.append(", ");
		}
		sb.append("]");
		return sb.toString();
	}
}