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.io.*;
import java.math.*;
import java.util.*;
public class Main {
	static int[] str; //Segment tree of rows
	static int[] stc; //Segment tree of columns
	static int[] rows;
	static int[] cols;
	public static void main(String[] args) { 
		/*
		 * */
		FastScanner I = new FastScanner(); //Input
		OutPut O = new OutPut(); //Output
		int N = I.nextInt();
		int Q = I.nextInt();
		long ans = N-2;
		ans*=ans;
		str = new int[4*N];
		stc = new int[4*N];
		rows = new int[N];
		cols = new int[N];
		while (Q-->0) {
			int op = I.nextInt();
			if (op==1) {
				int col = I.nextInt()-1;
				int lo = 0;
				int hi = N-2;
				int sub = 0;
				while (lo<=hi) { //Extending white stones downward
					int mid = (lo+hi)/2;
					int max = getMax(1,0,N-1,0,mid,stc);
					if (max<col) {
						sub=max(sub,mid);
						lo=mid+1;
					}else hi=mid-1;
				}
				cols[col]=max(cols[col],sub);
				UPD(1,0,N-1,col,sub,str);
				ans-=sub;
				//O.pln(sub);
			}else { //Horizontal extension of white stones
				int row = I.nextInt()-1;
				int lo = 0;
				int hi = N-2;
				int sub = 0;
				while (lo<=hi) {
					int mid = (lo+hi)/2;
					int max = getMax(1,0,N-1,0,mid,str);
					if (max<row) {
						sub=max(sub,mid);
						lo=mid+1;
					}else hi=mid-1;
				}
				rows[row]=max(rows[row],sub);
				UPD(1,0,N-1,row,sub,stc);
				ans-=sub;
				//O.pln(sub);
			}
		}
		O.pln(ans);
	}
	public static void UPD(int node, int start, int end, int in, int val, int[] st) {
		if (start==end) st[node]=val;
		else {
			int mid = (start+end)/2;
			if (in>=start&&in<=mid) {
				UPD(2*node,start,mid,in,val,st);
			}else {
				UPD(2*node+1,mid+1,end,in,val,st);
			}
			st[node]=max(st[2*node],st[2*node+1]);
		}
	}
	public static int getMax(int node, int start, int end,int L, int R, int[] st) {
		if (start>R||end<L) return 0;
		if (L<=start&&R>=end) return st[node];
		int mid = (start+end)/2;
		int left = getMax(2*node,start,mid,L,R,st);
		int right = getMax(2*node+1,mid+1,end,L,R,st);
		return max(left,right);
	}
	public static double max(double a, double b) {return Math.max(a, b);}
	public static double min(double a, double b) {return Math.min(a, b);}
	public static long min(long a, long b) {return Math.min(a,b);}
	public static long max(long a, long b) {return Math.max(a,b);}
	public static int min(int a, int b) {return Math.min(a,b);}
	public static int max(int a, int b) {return Math.max(a,b);}
	public static long abs(long x) {return Math.abs(x);}
	public static long ceil(long num, long den) {long ans = num/den; if (num%den!=0) 
	ans++; return ans;}
	public static long GCD(long a, long b) {
		if (a==0||b==0) return max(a,b);
		return GCD(min(a,b),max(a,b)%min(a,b));
	}
	public static long FastExp(long base, long exp, long mod) {
		long ans=1;
		while (exp>0) {
			if (exp%2==1) ans*=base;
			exp/=2;
			base*=base;
			base%=mod;
			ans%=mod;
		}
		return ans;
	}
	public static long ModInv(long num,long mod) {return FastExp(num,mod-2,mod);}
	public static int pop(long x) { //Returns number of bits within a number
		int cnt = 0;
		while (x>0) {
			if (x%2==1) cnt++;
			x/=2;
		}
		return cnt;
	}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());};
		double nextDouble() {return Double.parseDouble(next());}
	}
	static class OutPut{
		PrintWriter w = new PrintWriter(System.out);
		void pln(double x) {w.println(x);w.flush();}
		void pln(boolean x) {w.println(x);w.flush();}
		void pln(int x) {w.println(x);w.flush();}
		void pln(long x) {w.println(x);w.flush();}
		void pln(String x) {w.println(x);w.flush();}
		void pln(char x) {w.println(x);w.flush();}
		void pln(StringBuilder x) {w.println(x);w.flush();}
		void pln(BigInteger x) {w.println(x);w.flush();}
		void p(int x) {w.print(x);w.flush();}
		void p(long x) {w.print(x);w.flush();}
		void p(String x) {w.print(x);w.flush();}
		void p(char x) {w.print(x);w.flush();}
		void p(StringBuilder x) {w.print(x);w.flush();}
		void p(BigInteger x) {w.print(x);w.flush();}
		void p(double x) {w.print(x);w.flush();}
		void p(boolean x) {w.print(x);w.flush();}
	}
}