Recently in school Alina has learned what are the persistent data structures: they are data structures that always preserves the previous version of itself and access to it when it is modified.

After reaching home Alina decided to invent her own persistent data structure. Inventing didn't take long: there is a bookcase right behind her bed. Alina thinks that the bookcase is a good choice for a persistent data structure. Initially the bookcase is empty, thus there is no book at any position at any shelf.

The bookcase consists of n shelves, and each shelf has exactly m positions for books at it. Alina enumerates shelves by integers from 1 to n and positions at shelves — from 1 to m. Initially the bookcase is empty, thus there is no book at any position at any shelf in it.

Alina wrote down q operations, which will be consecutively applied to the bookcase. Each of the operations has one of four types:

  * 1 i j — Place a book at position j at shelf i if there is no book at it.
  * 2 i j — Remove the book from position j at shelf i if there is a book at it.
  * 3 i — Invert book placing at shelf i. This means that from every position at shelf i which has a book at it, the book should be removed, and at every position at shelf i which has not book at it, a book should be placed.
  * 4 k — Return the books in the bookcase in a state they were after applying k-th operation. In particular, k = 0 means that the bookcase should be in initial state, thus every book in the bookcase should be removed from its position.



After applying each of operation Alina is interested in the number of books in the bookcase. Alina got 'A' in the school and had no problem finding this values. Will you do so?

Input

The first line of the input contains three integers n, m and q (1 ≤ n, m ≤ 103, 1 ≤ q ≤ 105) — the bookcase dimensions and the number of operations respectively.

The next q lines describes operations in chronological order — i-th of them describes i-th operation in one of the four formats described in the statement.

It is guaranteed that shelf indices and position indices are correct, and in each of fourth-type operation the number k corresponds to some operation before it or equals to 0.

Output

For each operation, print the number of books in the bookcase after applying it in a separate line. The answers should be printed in chronological order.

Examples

Input

2 3 3
1 1 1
3 2
4 0


Output

1
4
0


Input

4 2 6
3 2
2 2 2
3 3
3 2
2 2 2
3 2


Output

2
1
3
3
2
4


Input

2 2 2
3 2
2 2 1


Output

2
1

Note

<image>

This image illustrates the second sample case.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        int n;
        int m;
        int q;
        int[] op;
        int[] row;
        int[] col;
        int[] answer;
        Graph gr;
        boolean[][] mat;
        int cntBooks;

        void dfs(int v) {
            boolean doOp = false;
            int idOP = v - 1;
            int row = idOP == -1 ? -1 : this.row[idOP];
            int col = idOP == -1 ? -1 : this.col[idOP];
            if (idOP != -1) {
                if (op[idOP] == 1) {
                    if (!mat[row][col]) {
                        mat[row][col] = true;
                        ++cntBooks;
                        doOp = true;
                    }
                } else if (op[idOP] == 2) {
                    if (mat[row][col]) {
                        mat[row][col] = false;
                        --cntBooks;
                        doOp = true;
                    }
                } else if (op[idOP] == 3) {
                    doOp = true;
                    for (int c = 0; c < m; c++) {
                        if (mat[row][c]) {
                            --cntBooks;
                        } else {
                            ++cntBooks;
                        }
                        mat[row][c] ^= true;
                    }
                }
            }

            if (idOP != -1) {
                answer[idOP] = cntBooks;
            }

            for (int id = gr.firstOutbound(v); id != -1; id = gr.nextOutbound(id)) {
                dfs(gr.destination(id));
                if (idOP != -1) {
                    if (answer[idOP] != cntBooks) {
                        throw new RuntimeException();
                    }
                }
            }

            if (doOp) {
                if (op[idOP] == 1) {
                    mat[row][col] = false;
                    --cntBooks;
                } else if (op[idOP] == 2) {
                    mat[row][col] = true;
                    ++cntBooks;
                } else if (op[idOP] == 3) {
                    for (int c = 0; c < m; c++) {
                        if (mat[row][c]) {
                            --cntBooks;
                        } else {
                            ++cntBooks;
                        }
                        mat[row][c] ^= true;
                    }
                }
            }

        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            n = in.readInt();
            m = in.readInt();
            q = in.readInt();

            row = new int[q];
            op = new int[q];
            col = new int[q];

            gr = new Graph(q + 1, q);
            for (int i = 0; i < q; i++) {
                op[i] = in.readInt();
                if (op[i] <= 2) {
                    row[i] = in.readInt() - 1;
                    col[i] = in.readInt() - 1;
                } else if (op[i] == 3) {
                    row[i] = in.readInt() - 1;
                } else {
                    row[i] = in.readInt();
                }
                if (op[i] == 4) {
                    gr.addSimpleEdge(row[i], i + 1);
                } else {
                    gr.addSimpleEdge(i, i + 1);
                }
            }

            mat = new boolean[n][m];
            answer = new int[q];
            dfs(0);
            for (int x : answer) {
                out.printLine(x);
            }
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(int i) {
            writer.println(i);
        }

    }

    static class Graph {
        public static final int REMOVED_BIT = 0;
        protected int vertexCount;
        protected int edgeCount;
        private int[] firstOutbound;
        private int[] firstInbound;
        private Edge[] edges;
        private int[] nextInbound;
        private int[] nextOutbound;
        private int[] from;
        private int[] to;
        private long[] weight;
        public long[] capacity;
        private int[] reverseEdge;
        private int[] flags;

        public Graph(int vertexCount) {
            this(vertexCount, vertexCount);
        }

        public Graph(int vertexCount, int edgeCapacity) {
            this.vertexCount = vertexCount;
            firstOutbound = new int[vertexCount];
            Arrays.fill(firstOutbound, -1);

            from = new int[edgeCapacity];
            to = new int[edgeCapacity];
            nextOutbound = new int[edgeCapacity];
            flags = new int[edgeCapacity];
        }

        public int addEdge(int fromID, int toID, long weight, long capacity, int reverseEdge) {
            ensureEdgeCapacity(edgeCount + 1);
            if (firstOutbound[fromID] != -1) {
                nextOutbound[edgeCount] = firstOutbound[fromID];
            } else {
                nextOutbound[edgeCount] = -1;
            }
            firstOutbound[fromID] = edgeCount;
            if (firstInbound != null) {
                if (firstInbound[toID] != -1) {
                    nextInbound[edgeCount] = firstInbound[toID];
                } else {
                    nextInbound[edgeCount] = -1;
                }
                firstInbound[toID] = edgeCount;
            }
            this.from[edgeCount] = fromID;
            this.to[edgeCount] = toID;
            if (capacity != 0) {
                if (this.capacity == null) {
                    this.capacity = new long[from.length];
                }
                this.capacity[edgeCount] = capacity;
            }
            if (weight != 0) {
                if (this.weight == null) {
                    this.weight = new long[from.length];
                }
                this.weight[edgeCount] = weight;
            }
            if (reverseEdge != -1) {
                if (this.reverseEdge == null) {
                    this.reverseEdge = new int[from.length];
                    Arrays.fill(this.reverseEdge, 0, edgeCount, -1);
                }
                this.reverseEdge[edgeCount] = reverseEdge;
            }
            if (edges != null) {
                edges[edgeCount] = createEdge(edgeCount);
            }
            return edgeCount++;
        }

        protected final GraphEdge createEdge(int id) {
            return new GraphEdge(id);
        }

        public final int addFlowWeightedEdge(int from, int to, long weight, long capacity) {
            if (capacity == 0) {
                return addEdge(from, to, weight, 0, -1);
            } else {
                int lastEdgeCount = edgeCount;
                addEdge(to, from, -weight, 0, lastEdgeCount + entriesPerEdge());
                return addEdge(from, to, weight, capacity, lastEdgeCount);
            }
        }

        protected int entriesPerEdge() {
            return 1;
        }

        public final int addWeightedEdge(int from, int to, long weight) {
            return addFlowWeightedEdge(from, to, weight, 0);
        }

        public final int addSimpleEdge(int from, int to) {
            return addWeightedEdge(from, to, 0);
        }

        public final int firstOutbound(int vertex) {
            int id = firstOutbound[vertex];
            while ((id != -1) && isRemoved(id)) {
                id = nextOutbound[id];
            }
            return id;
        }

        public final int nextOutbound(int id) {
            id = nextOutbound[id];
            while ((id != -1) && isRemoved(id)) {
                id = nextOutbound[id];
            }
            return id;
        }

        public final int destination(int id) {
            return to[id];
        }

        public final boolean flag(int id, int bit) {
            return ((flags[id] >> bit) & 1) != 0;
        }

        public final boolean isRemoved(int id) {
            return flag(id, REMOVED_BIT);
        }

        protected void ensureEdgeCapacity(int size) {
            if (from.length < size) {
                int newSize = Math.max(size, 2 * from.length);
                if (edges != null) {
                    edges = resize(edges, newSize);
                }
                from = resize(from, newSize);
                to = resize(to, newSize);
                nextOutbound = resize(nextOutbound, newSize);
                if (nextInbound != null) {
                    nextInbound = resize(nextInbound, newSize);
                }
                if (weight != null) {
                    weight = resize(weight, newSize);
                }
                if (capacity != null) {
                    capacity = resize(capacity, newSize);
                }
                if (reverseEdge != null) {
                    reverseEdge = resize(reverseEdge, newSize);
                }
                flags = resize(flags, newSize);
            }
        }

        protected final int[] resize(int[] array, int size) {
            int[] newArray = new int[size];
            System.arraycopy(array, 0, newArray, 0, array.length);
            return newArray;
        }

        private long[] resize(long[] array, int size) {
            long[] newArray = new long[size];
            System.arraycopy(array, 0, newArray, 0, array.length);
            return newArray;
        }

        private Edge[] resize(Edge[] array, int size) {
            Edge[] newArray = new Edge[size];
            System.arraycopy(array, 0, newArray, 0, array.length);
            return newArray;
        }

        protected class GraphEdge implements Edge {
            protected int id;

            protected GraphEdge(int id) {
                this.id = id;
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if ((c < '0') || (c > '9')) {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return (c == ' ') || (c == '\n') || (c == '\r') || (c == '\t') || (c == -1);
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static interface Edge {
    }
}

