Problem: For a given set of two-dimensional points S, let's denote its extension E(S) as the result of the following algorithm:

Create another set of two-dimensional points R, which is initially equal to S. Then, while there exist four numbers x_1, y_1, x_2 and y_2 such that (x_1, y_1) ∈ R, (x_1, y_2) ∈ R, (x_2, y_1) ∈ R and (x_2, y_2) ∉ R, add (x_2, y_2) to R. When it is impossible to find such four integers, let R be the result of the algorithm.

Now for the problem itself. You are given a set of two-dimensional points S, which is initially empty. You have to process two types of queries: add some point to S, or remove some point from it. After each query you have to compute the size of E(S).

Input

The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.

Then q lines follow, each containing two integers x_i, y_i (1 ≤ x_i, y_i ≤ 3 ⋅ 10^5), denoting i-th query as follows: if (x_i, y_i) ∈ S, erase it from S, otherwise insert (x_i, y_i) into S.

Output

Print q integers. i-th integer should be equal to the size of E(S) after processing first i queries.

Example

Input


7
1 1
1 2
2 1
2 2
1 2
1 3
2 1


Output


1 2 4 4 4 6 3 

Solution (in JAVA):

Solution:


import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.nio.charset.Charset;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Deque;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class CF1140F {
    public static void main(String[] args) throws Exception {
        boolean local = System.getProperty("ONLINE_JUDGE") == null;
        boolean async = false;

        Charset charset = Charset.forName("ascii");

        FastIO io = local ? new FastIO(new FileInputStream("D:\\DATABASE\\TESTCASE\\Code.in"), System.out, charset) : new FastIO(System.in, System.out, charset);
        Task task = new Task(io, new Debug(local));

        if (async) {
            Thread t = new Thread(null, task, "dalt", 1 << 27);
            t.setPriority(Thread.MAX_PRIORITY);
            t.start();
            t.join();
        } else {
            task.run();
        }

        if (local) {
            io.cache.append("\n\n--memory -- \n" + ((Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) >> 20) + "M");
        }

        io.flush();
    }

    public static class Task implements Runnable {
        final FastIO io;
        final Debug debug;
        int inf = (int) 1e8;
        int limit = 300000;
        long[] result;
        Deque<Line> stack = new ArrayDeque<>(limit);
        long total;


        public Task(FastIO io, Debug debug) {
            this.io = io;
            this.debug = debug;
        }

        @Override
        public void run() {
            solve();
        }

        public void solve() {
            int n = io.readInt();
            Map<Point, Event> point2event = new HashMap<>(n);
            List<Event> eventList = new ArrayList<>(n);
            Line[] xLines = new Line[limit + 1];
            Line[] yLines = new Line[limit + 1];
            result = new long[n + 1];
            for (int i = 1; i <= limit; i++) {
                xLines[i] = new Line();
                xLines[i].row = 1;
                yLines[i] = new Line();
                yLines[i].col = 1;
            }
            for (int i = 1; i <= n; i++) {
                Point point = new Point();
                point.x = io.readInt();
                point.y = io.readInt();
                Event event = point2event.get(point);
                if (event == null) {
                    event = new Event();
                    event.lineX = xLines[point.x];
                    event.lineY = yLines[point.y];
                    event.l = i;
                    point2event.put(point, event);
                } else {
                    event.r = i - 1;
                    point2event.remove(point);
                    eventList.add(event);
                }
            }
            for (Event event : point2event.values()) {
                event.r = n;
                eventList.add(event);
            }

            Segment root = Segment.build(1, n);
            for (Event event : eventList) {
                Segment.update(event.l, event.r, 1, n, event, root);
            }

            dfs(root, 1, n);
            for (int i = 1; i <= n; i++) {
                io.cache.append(result[i]).append(' ');
            }
        }

        public void dfs(Segment segment, int l, int r) {
            int sp = stack.size();
            for (Event event : segment.events) {
                total += Line.union(event.lineX, event.lineY, stack);
            }
            if (l < r) {
                int m = (l + r) >> 1;
                dfs(segment.left, l, m);
                dfs(segment.right, m + 1, r);
            } else {
                result[l] = total;
            }
            while (stack.size() > sp) {
                total += Line.remove(stack.removeLast());
            }
        }
    }

    public static class Segment implements Cloneable {
        Segment left;
        Segment right;
        List<Event> events = new ArrayList<>();

        public static Segment build(int l, int r) {
            Segment segment = new Segment();
            if (l != r) {
                int m = (l + r) >> 1;
                segment.left = build(l, m);
                segment.right = build(m + 1, r);
            }
            return segment;
        }

        public static boolean checkOutOfRange(int ll, int rr, int l, int r) {
            return ll > r || rr < l;
        }

        public static boolean checkCoverage(int ll, int rr, int l, int r) {
            return ll <= l && rr >= r;
        }

        public static void update(int ll, int rr, int l, int r, Event event, Segment segment) {
            if (checkOutOfRange(ll, rr, l, r)) {
                return;
            }
            if (checkCoverage(ll, rr, l, r)) {
                segment.events.add(event);
                return;
            }
            int m = (l + r) >> 1;

            update(ll, rr, l, m, event, segment.left);
            update(ll, rr, m + 1, r, event, segment.right);
        }
    }

    public static class Line {
        Line parent;
        int rank = 1;
        int row;
        int col;

        public Line findSet() {
            return parent == null ? this : parent.findSet();
        }

        public long intersect() {
            return (long)row * col;
        }

        public static long remove(Line line) {
            if (line.parent == null) {
                return 0;
            }

            Line p = line.parent;
            line.parent = null;

            long diff = 0;
            while (p != null) {
                diff = -p.intersect();
                p.row -= line.row;
                p.col -= line.col;
                p.rank -= line.rank;
                diff += p.intersect();
                p = p.parent;
            }

            return diff + line.intersect();
        }

        public static long union(Line a, Line b, Deque<Line> undo) {
            a = a.findSet();
            b = b.findSet();
            if (a == b) {
                return 0;
            }
            if (a.rank < b.rank) {
                Line c = a;
                a = b;
                b = c;
            }
            long old = a.intersect() + b.intersect();
            b.parent = a;
            a.rank += b.rank;
            a.row += b.row;
            a.col += b.col;
            undo.addLast(b);
            return a.intersect() - old;
        }
    }

    public static class Point {
        int x;
        int y;

        @Override
        public int hashCode() {
            return x * 31 + y;
        }

        @Override
        public boolean equals(Object obj) {
            Point pt = (Point) obj;
            return x == pt.x && y == pt.y;
        }
    }

    public static class Event {
        int l;
        int r;
        Line lineX;
        Line lineY;
    }

    public static class FastIO {
        public final StringBuilder cache = new StringBuilder();
        private final InputStream is;
        private final OutputStream os;
        private final Charset charset;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 8);
        private byte[] buf = new byte[1 << 23];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastIO(InputStream is, OutputStream os, Charset charset) {
            this.is = is;
            this.os = os;
            this.charset = charset;
        }

        public FastIO(InputStream is, OutputStream os) {
            this(is, os, Charset.forName("ascii"));
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public long readLong() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            long val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public double readDouble() {
            boolean sign = true;
            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+';
                next = read();
            }

            long val = 0;
            while (next >= '0' && next <= '9') {
                val = val * 10 + next - '0';
                next = read();
            }
            if (next != '.') {
                return sign ? val : -val;
            }
            next = read();
            long radix = 1;
            long point = 0;
            while (next >= '0' && next <= '9') {
                point = point * 10 + next - '0';
                radix = radix * 10;
                next = read();
            }
            double result = val + (double) point / radix;
            return sign ? result : -result;
        }

        public String readString(StringBuilder builder) {
            skipBlank();

            while (next > 32) {
                builder.append((char) next);
                next = read();
            }

            return builder.toString();
        }

        public String readString() {
            defaultStringBuf.setLength(0);
            return readString(defaultStringBuf);
        }

        public int readLine(char[] data, int offset) {
            int originalOffset = offset;
            while (next != -1 && next != '\n') {
                data[offset++] = (char) next;
                next = read();
            }
            return offset - originalOffset;
        }

        public int readString(char[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (char) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public int readString(byte[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (byte) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public char readChar() {
            skipBlank();
            char c = (char) next;
            next = read();
            return c;
        }

        public void flush() {
            try {
                os.write(cache.toString().getBytes(charset));
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public boolean hasMore() {
            skipBlank();
            return next != -1;
        }
    }

    public static class Debug {
        private boolean allowDebug;

        public Debug(boolean allowDebug) {
            this.allowDebug = allowDebug;
        }

        public void assertTrue(boolean flag) {
            if (!allowDebug) {
                return;
            }
            if (!flag) {
                fail();
            }
        }

        public void fail() {
            throw new RuntimeException();
        }

        public void assertFalse(boolean flag) {
            if (!allowDebug) {
                return;
            }
            if (flag) {
                fail();
            }
        }

        private void outputName(String name) {
            System.out.print(name + " = ");
        }

        public void debug(String name, int x) {
            if (!allowDebug) {
                return;
            }

            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, long x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, double x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, int[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, long[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, double[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, Object x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, Object... x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.deepToString(x));
        }
    }
}