Vasya has the square chessboard of size n × n and m rooks. Initially the chessboard is empty. Vasya will consequently put the rooks on the board one after another.

The cell of the field is under rook's attack, if there is at least one rook located in the same row or in the same column with this cell. If there is a rook located in the cell, this cell is also under attack.

You are given the positions of the board where Vasya will put rooks. For each rook you have to determine the number of cells which are not under attack after Vasya puts it on the board.

Input

The first line of the input contains two integers n and m (1 ≤ n ≤ 100 000, 1 ≤ m ≤ min(100 000, n2)) — the size of the board and the number of rooks. 

Each of the next m lines contains integers xi and yi (1 ≤ xi, yi ≤ n) — the number of the row and the number of the column where Vasya will put the i-th rook. Vasya puts rooks on the board in the order they appear in the input. It is guaranteed that any cell will contain no more than one rook.

Output

Print m integer, the i-th of them should be equal to the number of cells that are not under attack after first i rooks are put.

Examples

Input

3 3
1 1
3 1
2 2


Output

4 2 0 


Input

5 2
1 5
5 1


Output

16 9 


Input

100000 1
300 400


Output

9999800001 

Note

On the picture below show the state of the board after put each of the three rooks. The cells which painted with grey color is not under the attack.

<image>
//package baobab;
import java.io.*;
import java.util.*;

public class B {

    public static void main(String[] args) {
        BIO io = new BIO();
        try {
            Bsolver solver = new Bsolver(io);
            solver.solve();
        } finally {
            io.close();
        }
    }

}

class Bsolver {
    BIO io;

    public Bsolver(BIO io) {
        this.io = io;
    }

    public void solve() {
        int n = io.nextInt();
        int m = io.nextInt();
        HashSet<Integer> xBah = new HashSet<>();
        HashSet<Integer> yBah = new HashSet<>();
        int[] hitsY = new int[n+1];
        int[] hitsX = new int[n+1];
        long countFree = ((long) n) * n;
        for (int i=0; i<m; i++) {
            int y = io.nextInt();
            int x = io.nextInt();
            Integer newThreats;
            if (hitsY[y] == 0 && hitsX[x] == 0) {
                newThreats = n + n - 1 - xBah.size() - yBah.size();
            } else if (hitsY[y] == 0) {
                newThreats = n - 1 - (xBah.size() - 1);
            } else if (hitsX[x] == 0) {
                newThreats = n - 1 - (yBah.size() - 1);
            } else {
                newThreats = 0;
            }
            countFree -= newThreats;
            hitsY[y]++;
            hitsX[x]++;
            xBah.add(x);
            yBah.add(y);
            io.print(countFree + " ");
        }
        io.println();
    }

    private static class Pair implements Comparable<Pair> {
        int id;
        long val;

        public Pair(long val, int id) {
            this.val = val;
            this.id = id;
        }

        @Override
        public int compareTo(Pair o) {
            if (this.val < o.val) return -1;
            if (this.val > o.val) return 1;
            return this.id - o.id;
        }
    }

    /* Reads n-1 edges by default. */
    private List<Integer>[] toGraph(BIO io, int n) {
        List<Integer>[] g = new ArrayList[n+1];
        for (int i=1; i<=n; i++) g[i] = new ArrayList<>();
        for (int i=1; i<=n-1; i++) {
            int a = io.nextInt();
            int b = io.nextInt();
            g[a].add(b);
            g[b].add(a);
        }
        return g;
    }
}

class BIO extends PrintWriter {
    private InputStreamReader r;
    private static final int BUFSIZE = 1 << 15;
    private char[] buf;
    private int bufc;
    private int bufi;
    private StringBuilder sb;

    public BIO() {
        super(new BufferedOutputStream(System.out));
        r = new InputStreamReader(System.in);

        buf = new char[BUFSIZE];
        bufc = 0;
        bufi = 0;
        sb = new StringBuilder();
    }

    private void fillBuf() throws IOException {
        bufi = 0;
        bufc = 0;
        while(bufc == 0) {
            bufc = r.read(buf, 0, BUFSIZE);
            if(bufc == -1) {
                bufc = 0;
                return;
            }
        }
    }

    private boolean pumpBuf() throws IOException {
        if(bufi == bufc) {
            fillBuf();
        }
        return bufc != 0;
    }

    private boolean isDelimiter(char c) {
        return c == ' ' || c == '\t' || c == '\n' || c == '\r' || c == '\f';
    }

    private void eatDelimiters() throws IOException {
        while(true) {
            if(bufi == bufc) {
                fillBuf();
                if(bufc == 0) throw new RuntimeException("IO: Out of input.");
            }

            if(!isDelimiter(buf[bufi])) break;
            ++bufi;
        }
    }

    public String next() {
        try {
            sb.setLength(0);

            eatDelimiters();
            int start = bufi;

            while(true) {
                if(bufi == bufc) {
                    sb.append(buf, start, bufi - start);
                    fillBuf();
                    start = 0;
                    if(bufc == 0) break;
                }

                if(isDelimiter(buf[bufi])) break;
                ++bufi;
            }

            sb.append(buf, start, bufi - start);

            return sb.toString();
        } catch(IOException e) {
            throw new RuntimeException("IO.next: Caught IOException.");
        }
    }

    public int nextInt() {
        try {
            int ret = 0;

            eatDelimiters();

            boolean positive = true;
            if(buf[bufi] == '-') {
                ++bufi;
                if(!pumpBuf()) throw new RuntimeException("IO.nextInt: Invalid int.");
                positive = false;
            }

            boolean first = true;
            while(true) {
                if(!pumpBuf()) break;
                if(isDelimiter(buf[bufi])) {
                    if(first) throw new RuntimeException("IO.nextInt: Invalid int.");
                    break;
                }
                first = false;

                if(buf[bufi] >= '0' && buf[bufi] <= '9') {
                    if(ret < -214748364) throw new RuntimeException("IO.nextInt: Invalid int.");
                    ret *= 10;
                    ret -= (int)(buf[bufi] - '0');
                    if(ret > 0) throw new RuntimeException("IO.nextInt: Invalid int.");
                } else {
                    throw new RuntimeException("IO.nextInt: Invalid int.");
                }

                ++bufi;
            }

            if(positive) {
                if(ret == -2147483648) throw new RuntimeException("IO.nextInt: Invalid int.");
                ret = -ret;
            }

            return ret;
        } catch(IOException e) {
            throw new RuntimeException("IO.nextInt: Caught IOException.");
        }
    }

    public long nextLong() {
        try {
            long ret = 0;

            eatDelimiters();

            boolean positive = true;
            if(buf[bufi] == '-') {
                ++bufi;
                if(!pumpBuf()) throw new RuntimeException("IO.nextLong: Invalid long.");
                positive = false;
            }

            boolean first = true;
            while(true) {
                if(!pumpBuf()) break;
                if(isDelimiter(buf[bufi])) {
                    if(first) throw new RuntimeException("IO.nextLong: Invalid long.");
                    break;
                }
                first = false;

                if(buf[bufi] >= '0' && buf[bufi] <= '9') {
                    if(ret < -922337203685477580L) throw new RuntimeException("IO.nextLong: Invalid long.");
                    ret *= 10;
                    ret -= (long)(buf[bufi] - '0');
                    if(ret > 0) throw new RuntimeException("IO.nextLong: Invalid long.");
                } else {
                    throw new RuntimeException("IO.nextLong: Invalid long.");
                }

                ++bufi;
            }

            if(positive) {
                if(ret == -9223372036854775808L) throw new RuntimeException("IO.nextLong: Invalid long.");
                ret = -ret;
            }

            return ret;
        } catch(IOException e) {
            throw new RuntimeException("IO.nextLong: Caught IOException.");
        }
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

}