Recently, Tokitsukaze found an interesting game. Tokitsukaze had n items at the beginning of this game. However, she thought there were too many items, so now she wants to discard m (1 ≤ m ≤ n) special items of them.

These n items are marked with indices from 1 to n. In the beginning, the item with index i is placed on the i-th position. Items are divided into several pages orderly, such that each page contains exactly k positions and the last positions on the last page may be left empty.

Tokitsukaze would do the following operation: focus on the first special page that contains at least one special item, and at one time, Tokitsukaze would discard all special items on this page. After an item is discarded or moved, its old position would be empty, and then the item below it, if exists, would move up to this empty position. The movement may bring many items forward and even into previous pages, so Tokitsukaze would keep waiting until all the items stop moving, and then do the operation (i.e. check the special page and discard the special items) repeatedly until there is no item need to be discarded.

<image> Consider the first example from the statement: n=10, m=4, k=5, p=[3, 5, 7, 10]. The are two pages. Initially, the first page is special (since it is the first page containing a special item). So Tokitsukaze discards the special items with indices 3 and 5. After, the first page remains to be special. It contains [1, 2, 4, 6, 7], Tokitsukaze discards the special item with index 7. After, the second page is special (since it is the first page containing a special item). It contains [9, 10], Tokitsukaze discards the special item with index 10.

Tokitsukaze wants to know the number of operations she would do in total.

Input

The first line contains three integers n, m and k (1 ≤ n ≤ 10^{18}, 1 ≤ m ≤ 10^5, 1 ≤ m, k ≤ n) — the number of items, the number of special items to be discarded and the number of positions in each page.

The second line contains m distinct integers p_1, p_2, …, p_m (1 ≤ p_1 < p_2 < … < p_m ≤ n) — the indices of special items which should be discarded.

Output

Print a single integer — the number of operations that Tokitsukaze would do in total.

Examples

Input


10 4 5
3 5 7 10


Output


3


Input


13 4 5
7 8 9 10


Output


1

Note

For the first example:

  * In the first operation, Tokitsukaze would focus on the first page [1, 2, 3, 4, 5] and discard items with indices 3 and 5; 
  * In the second operation, Tokitsukaze would focus on the first page [1, 2, 4, 6, 7] and discard item with index 7; 
  * In the third operation, Tokitsukaze would focus on the second page [9, 10] and discard item with index 10. 



For the second example, Tokitsukaze would focus on the second page [6, 7, 8, 9, 10] and discard all special items at once.
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.util.Collection;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author aryssoncf
 */
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);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            try {
                long n = in.readLong();
                int m = in.readInt();
                long k = in.readLong();
                long[] p = in.readLongArray(m);
                MiscUtils.decreaseByOne(p);
                EzLongTreeSet set = new EzLongTreeSet(p);
                int rem = 0, res = 0;
                while (!set.isEmpty()) {
                    long x = set.getFirst(), page = getPage(x, k, rem);
                    int c = 0;
                    while (!set.isEmpty() && getPage(set.getFirst(), k, rem) == page) {
                        set.removeFirst();
                        c++;
                    }
                    rem += c;
                    res++;
                }
                out.printLine(res);
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        long getPage(long p, long k, int rem) {
            return (p - rem) / k;
        }

    }

    static interface EzLongCollection {
        int size();

        EzLongIterator iterator();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }

    static interface EzLongIterator {
        boolean hasNext();

        long next();

    }

    static final class PrimitiveHashCalculator {
        private PrimitiveHashCalculator() {
        }

        public static int getHash(long x) {
            return (int) x ^ (int) (x >>> 32);
        }

    }

    static interface EzLongSet extends EzLongCollection {
        int size();

        EzLongIterator iterator();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }

    static interface EzLongSortedSet extends EzLongSet {
        int size();

        EzLongIterator iterator();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }

    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 MiscUtils {
        public static void decreaseByOne(long[]... arrays) {
            for (long[] array : arrays) {
                for (int i = 0; i < array.length; i++) {
                    array[i]--;
                }
            }
        }

    }

    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 long[] readLongArray(int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; i++) {
                array[i] = readLong();
            }
            return array;
        }

        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 long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long 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 {
            boolean isSpaceChar(int ch);

        }

    }

    static class EzLongTreeSet implements EzLongSortedSet {
        private static final int DEFAULT_CAPACITY = 10;
        private static final double ENLARGE_SCALE = 2.0;
        private static final int HASHCODE_INITIAL_VALUE = 0x811c9dc5;
        private static final int HASHCODE_MULTIPLIER = 0x01000193;
        private static final boolean BLACK = false;
        private static final boolean RED = true;
        private static final int NULL = 0;
        private static final long DEFAULT_NULL_ELEMENT = (new long[1])[0];
        private long[] key;
        private int[] left;
        private int[] right;
        private int[] p;
        private boolean[] color;
        private int size;
        private int root;
        private boolean returnedNull;

        public EzLongTreeSet() {
            this(DEFAULT_CAPACITY);
        }

        public EzLongTreeSet(int capacity) {
            if (capacity < 0) {
                throw new IllegalArgumentException("Capacity must be non-negative");
            }
            capacity++;
            key = new long[capacity];
            left = new int[capacity];
            right = new int[capacity];
            p = new int[capacity];
            color = new boolean[capacity];
            color[NULL] = BLACK;
            size = 0;
            root = NULL;
            returnedNull = false;
        }

        public EzLongTreeSet(EzLongCollection collection) {
            this(collection.size());
            for (EzLongIterator iterator = collection.iterator(); iterator.hasNext(); ) {
                add(iterator.next());
            }
        }

        public EzLongTreeSet(long[] srcArray) {
            this(srcArray.length);
            for (long element : srcArray) {
                add(element);
            }
        }

        public EzLongTreeSet(Collection<Long> javaCollection) {
            this(javaCollection.size());
            for (long element : javaCollection) {
                add(element);
            }
        }

        public int size() {
            return size;
        }

        public boolean isEmpty() {
            return size == 0;
        }

        public EzLongIterator iterator() {
            return new EzLongTreeSetIterator();
        }

        public boolean add(long element) {
            int y = NULL;
            int x = root;
            while (x != NULL) {
                //noinspection SuspiciousNameCombination
                y = x;
                if (element < key[x]) {
                    x = left[x];
                } else if (element > key[x]) {
                    x = right[x];
                } else {
                    return false;
                }
            }
            if (size == color.length - 1) {
                enlarge();
            }
            int z = ++size;
            key[z] = element;
            p[z] = y;
            if (y == NULL) {
                root = z;
            } else {
                if (element < key[y]) {
                    left[y] = z;
                } else {
                    right[y] = z;
                }
            }
            left[z] = NULL;
            right[z] = NULL;
            color[z] = RED;
            fixAfterAdd(z);
            return true;
        }

        private void removeNode(int z) {
            int y = (left[z] == NULL || right[z] == NULL) ? z : successorNode(z);
            int x = (left[y] != NULL) ? left[y] : right[y];
            p[x] = p[y];
            if (p[y] == NULL) {
                root = x;
            } else {
                if (y == left[p[y]]) {
                    left[p[y]] = x;
                } else {
                    right[p[y]] = x;
                }
            }
            if (y != z) {
                key[z] = key[y];
            }
            //noinspection PointlessBooleanExpression
            if (color[y] == BLACK) {
                fixAfterRemove(x);
            }
            // Swap with last
            if (y != size) {
                // copy fields
                key[y] = key[size];
                left[y] = left[size];
                right[y] = right[size];
                p[y] = p[size];
                color[y] = color[size];
                // fix the children's parents
                p[left[size]] = y;
                p[right[size]] = y;
                // fix one of the parent's children
                if (left[p[size]] == size) {
                    left[p[size]] = y;
                } else {
                    right[p[size]] = y;
                }
                // fix root
                if (root == size) {
                    root = y;
                }
            }
            size--;
        }

        private int successorNode(int x) {
            if (right[x] != NULL) {
                x = right[x];
                while (left[x] != NULL) {
                    x = left[x];
                }
                return x;
            } else {
                int y = p[x];
                while (y != NULL && x == right[y]) {
                    //noinspection SuspiciousNameCombination
                    x = y;
                    y = p[y];
                }
                return y;
            }
        }

        private void fixAfterAdd(int z) {
            while (color[p[z]] == RED) {
                if (p[z] == left[p[p[z]]]) {
                    int y = right[p[p[z]]];
                    if (color[y] == RED) {
                        color[p[z]] = BLACK;
                        color[y] = BLACK;
                        color[p[p[z]]] = RED;
                        z = p[p[z]];
                    } else {
                        if (z == right[p[z]]) {
                            z = p[z];
                            rotateLeft(z);
                        }
                        color[p[z]] = BLACK;
                        color[p[p[z]]] = RED;
                        rotateRight(p[p[z]]);
                    }
                } else {
                    int y = left[p[p[z]]];
                    if (color[y] == RED) {
                        color[p[z]] = BLACK;
                        color[y] = BLACK;
                        color[p[p[z]]] = RED;
                        z = p[p[z]];
                    } else {
                        if (z == left[p[z]]) {
                            z = p[z];
                            rotateRight(z);
                        }
                        color[p[z]] = BLACK;
                        color[p[p[z]]] = RED;
                        rotateLeft(p[p[z]]);
                    }
                }
            }
            color[root] = BLACK;
        }

        private void fixAfterRemove(int x) {
            while (x != root && color[x] == BLACK) {
                if (x == left[p[x]]) {
                    int w = right[p[x]];
                    if (color[w] == RED) {
                        color[w] = BLACK;
                        color[p[x]] = RED;
                        rotateLeft(p[x]);
                        w = right[p[x]];
                    }
                    if (color[left[w]] == BLACK && color[right[w]] == BLACK) {
                        color[w] = RED;
                        x = p[x];
                    } else {
                        if (color[right[w]] == BLACK) {
                            color[left[w]] = BLACK;
                            color[w] = RED;
                            rotateRight(w);
                            w = right[p[x]];
                        }
                        color[w] = color[p[x]];
                        color[p[x]] = BLACK;
                        color[right[w]] = BLACK;
                        rotateLeft(p[x]);
                        x = root;
                    }
                } else {
                    int w = left[p[x]];
                    if (color[w] == RED) {
                        color[w] = BLACK;
                        color[p[x]] = RED;
                        rotateRight(p[x]);
                        w = left[p[x]];
                    }
                    if (color[left[w]] == BLACK && color[right[w]] == BLACK) {
                        color[w] = RED;
                        x = p[x];
                    } else {
                        if (color[left[w]] == BLACK) {
                            color[right[w]] = BLACK;
                            color[w] = RED;
                            rotateLeft(w);
                            w = left[p[x]];
                        }
                        color[w] = color[p[x]];
                        color[p[x]] = BLACK;
                        color[left[w]] = BLACK;
                        rotateRight(p[x]);
                        x = root;
                    }
                }
            }
            color[x] = BLACK;
        }

        private void rotateLeft(int x) {
            int y = right[x];
            right[x] = left[y];
            if (left[y] != NULL) {
                p[left[y]] = x;
            }
            p[y] = p[x];
            if (p[x] == NULL) {
                root = y;
            } else {
                if (x == left[p[x]]) {
                    left[p[x]] = y;
                } else {
                    right[p[x]] = y;
                }
            }
            left[y] = x;
            p[x] = y;
        }

        private void rotateRight(int x) {
            int y = left[x];
            left[x] = right[y];
            if (right[y] != NULL) {
                p[right[y]] = x;
            }
            p[y] = p[x];
            if (p[x] == NULL) {
                root = y;
            } else {
                if (x == right[p[x]]) {
                    right[p[x]] = y;
                } else {
                    left[p[x]] = y;
                }
            }
            right[y] = x;
            p[x] = y;
        }

        private void enlarge() {
            int newLength = Math.max(color.length + 1, (int) (color.length * ENLARGE_SCALE));
            key = Arrays.copyOf(key, newLength);
            left = Arrays.copyOf(left, newLength);
            right = Arrays.copyOf(right, newLength);
            p = Arrays.copyOf(p, newLength);
            color = Arrays.copyOf(color, newLength);
        }

        private int firstNode() {
            int x = root;
            while (left[x] != NULL) {
                x = left[x];
            }
            return x;
        }

        public long getFirst() {
            if (root == NULL) {
                returnedNull = true;
                return DEFAULT_NULL_ELEMENT;
            }
            final int x = firstNode();
            returnedNull = false;
            return key[x];
        }

        public long removeFirst() {
            if (root == NULL) {
                returnedNull = true;
                return DEFAULT_NULL_ELEMENT;
            }
            final int x = firstNode();
            returnedNull = false;
            final long removedElement = key[x];
            removeNode(x);
            return removedElement;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            EzLongTreeSet that = (EzLongTreeSet) o;

            if (size != that.size) {
                return false;
            }
            for (int x = firstNode(), y = that.firstNode();
                 x != NULL;
                //noinspection SuspiciousNameCombination
                 x = successorNode(x), y = that.successorNode(y)
            ) {
                if (key[x] != that.key[y]) {
                    return false;
                }
            }
            return true;
        }

        public int hashCode() {
            int hash = HASHCODE_INITIAL_VALUE;
            for (int x = firstNode(); x != NULL; x = successorNode(x)) {
                hash = (hash ^ PrimitiveHashCalculator.getHash(key[x])) * HASHCODE_MULTIPLIER;
            }
            return hash;
        }

        public String toString() {
            StringBuilder sb = new StringBuilder();
            sb.append('[');
            for (int x = firstNode(); x != NULL; x = successorNode(x)) {
                if (sb.length() > 1) {
                    sb.append(", ");
                }
                sb.append(key[x]);
            }
            sb.append(']');
            return sb.toString();
        }

        private class EzLongTreeSetIterator implements EzLongIterator {
            private int x;

            private EzLongTreeSetIterator() {
                x = firstNode();
            }

            public boolean hasNext() {
                return x != NULL;
            }

            public long next() {
                if (x == NULL) {
                    throw new NoSuchElementException("Iterator doesn't have more elements");
                }
                final long result = key[x];
                x = successorNode(x);
                return result;
            }

        }

    }
}

