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.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		var sc = new Scanner(System.in);
		var n = sc.nextInt();
		var q = sc.nextInt();
		var q1 = new int[q];
		var q2 = new int[q];
		for (var i = 0; i < q; i++) {
			q1[i] = sc.nextInt();
			q2[i] = sc.nextInt();
		}
		sc.close();

		var sum = (long) (n - 2) * (n - 2);
		var x = new HashMap<Integer, Integer>();
		var y = new HashMap<Integer, Integer>();
		var x2 = new Main().new SortedList();
		var y2 = new Main().new SortedList();
		x.put(n, n);
		y.put(n, n);
		x2.add(n);
		y2.add(n);
		for (var i = 0; i < q; i++) {
			var qt = q1[i];
			var qv = q2[i];
			if (qt == 1) {
				var v = search(x, x2, qv, n);
				sum -= v - 2;
				update(y, y2, v, qv);
			} else {
				var v = search(y, y2, qv, n);
				sum -= v - 2;
				update(x, x2, v, qv);
			}
		}
		System.out.println(sum);
	}

	private static int search(HashMap<Integer, Integer> map, SortedList list, int key, int n) {
		var mapKey = list.searchValue(key);
		var result = map.get(mapKey);
		return result;
	}

	private static void update(HashMap<Integer, Integer> map, SortedList list, int key, int value) {
		if (map.containsKey(key)) {
			map.put(key, Math.min(map.get(key), value));
			list.add(key);
		} else {
			map.put(key, value);
			list.add(key);
		}
	}

	public class SortedList {
		List<Integer> list;

		public SortedList() {
			this.list = new ArrayList<Integer>();
		}

		public SortedList(List<Integer> list) {
			this.list = list;
		}

		public int get(int index) {
			return list.get(index);
		}

		public void add(int value) {
			list.add(search(value), value);
		}

		public int remove(int index) {
			return list.remove(index);
		}

		public int searchValue(int value) {
			return list.get(search(value));
		}

		private int search(int value) {
			var min = 0;
			var max = list.size();
			while (max - min > 1) {
				var mid = min + (max - min) / 2;
				if (list.get(mid) <= value) {
					min = mid;
				} else {
					max = mid;
				}
			}

			if (max - min == 1 && list.get(min) <= value) {
				min++;
			}
			return min;
		}
	}
}