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.*;

public class Main {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int n = sc.nextInt();
        int q = sc.nextInt();
        RangeTree v = new RangeTree(n + 1);
        RangeTree h = new RangeTree(n + 1);
        for (int i = 1; i <= n; i++) {
            v.update(i, i, n);
            h.update(i, i, n);
        }
        long res = (n - 2) * ((long)n - 2);
        for (int i = 0; i < q; i++) {
            int type = sc.nextInt(); int x = sc.nextInt();
            if (type == 1) {
                int to = (int) v.sumQuery(x, x);
                if (to <= 2) continue;
                long cur = h.minQuery(1, to - 1);
                if (x < cur) {
                    h.update(1, to - 1, x - cur);
                }
                v.update(x, x, 1 - to);
                res -= (to - 2);
            } else {
                int to = (int) h.sumQuery(x, x);
                if (to <= 2) continue;
                long cur = v.minQuery(1, to - 1);
                if (x < cur) {
                    v.update(1, to - 1, x - cur);
                }
                h.update(x, x, 1 - to);
                res -= (to - 2);
            }
        }
        out.println(res);
        out.close();
    }

    static class RangeTree {
        private long[] max;
        private long[] min;
        private long[] lazy;
        private long[] sum;
        private int size;
        public RangeTree(int size) {
            this.size = size;
            max = new long[4*size];
            min = new long[4*size];
            sum = new long[4*size];
            lazy = new long[4*size];
        }
        public void update(int l, int r, long inc) {
            update(1, 0, size-1, l, r, inc);
        }
        private void pushDown(int index, int l, int r) {
            min[index] += lazy[index];
            max[index] += lazy[index];
            sum[index] += lazy[index] * (r-l+1);
            if(l != r) {
                lazy[2*index] += lazy[index];
                lazy[2*index+1] += lazy[index];
            }
            lazy[index] = 0;
        }
        private void pullUp(int index, int l, int r) {
            int m = (l+r)/2;
            min[index] = Math.min(evaluateMin(2*index, l, m), evaluateMin(2*index+1, m+1, r));
            max[index] = Math.max(evaluateMax(2*index, l, m), evaluateMax(2*index+1, m+1, r));
            sum[index] = evaluateSum(2*index, l, m) + evaluateSum(2*index+1, m+1, r);
        }
        private long evaluateSum(int index, int l, int r) {
            return sum[index] + (r-l+1)*lazy[index];
        }
        private long evaluateMin(int index, int l, int r) {
            return min[index] + lazy[index];
        }
        private long evaluateMax(int index, int l, int r) {
            return max[index] + lazy[index];
        }
        private void update(int index, int l, int r, int left, int right, long inc) {
            if(r < left || l > right) return;
            if(l >= left && r <= right) {
                lazy[index] += inc;
                return;
            }
            pushDown(index, l, r);
            int m = (l+r)/2;
            update(2*index, l, m, left, right, inc);
            update(2*index+1, m+1, r, left, right, inc);
            pullUp(index, l, r);
        }
        public long minQuery(int l, int r) {
            return minQuery(1, 0, size-1, l, r);
        }
        private long minQuery(int index, int l, int r, int left, int right) {
            if(r < left || l > right) return Long.MAX_VALUE;
            if(l >= left && r <= right) {
                return evaluateMin(index, l, r);
            }
            pushDown(index, l, r);
            int m = (l+r)/2;
            long ret = Long.MAX_VALUE;
            ret = Math.min(ret, minQuery(2*index, l, m, left, right));
            ret = Math.min(ret, minQuery(2*index+1, m+1, r, left, right));
            pullUp(index, l, r);
            return ret;
        }
        public long maxQuery(int l, int r) {
            return maxQuery(1, 0, size-1, l, r);
        }
        private long maxQuery(int index, int l, int r, int left, int right) {
            if(r < left || l > right) return Long.MIN_VALUE;
            if(l >= left && r <= right) {
                return evaluateMax(index, l, r);
            }
            pushDown(index, l, r);
            int m = (l+r)/2;
            long ret = Long.MIN_VALUE;
            ret = Math.max(ret, maxQuery(2*index, l, m, left, right));
            ret = Math.max(ret, maxQuery(2*index+1, m+1, r, left, right));
            pullUp(index, l, r);
            return ret;
        }
        public long sumQuery(int l, int r) {
            return sumQuery(1, 0, size-1, l, r);
        }
        private long sumQuery(int index, int l, int r, int left, int right) {
            if(r < left || l > right) return 0;
            if(l >= left && r <= right) {
                return evaluateSum(index, l, r);
            }
            pushDown(index, l, r);
            int m = (l+r)/2;
            long ret = 0;
            ret += sumQuery(2*index, l, m, left, right);
            ret += sumQuery(2*index+1, m+1, r, left, right);
            pullUp(index, l, r);
            return ret;
        }
    }

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                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());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }


    }

}