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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.Objects;
import java.util.Queue;
import java.util.StringTokenizer;
import java.util.function.BiFunction;
import java.util.function.Function;

public class Main {

    static BiFunction<Integer, Integer, Integer> ADD = (x, y) -> (x + y);
    static BiFunction<ArrayList<Integer>, ArrayList<Integer>, ArrayList<Integer>> ADD_ARRAY_LIST = (x, y) -> {
        x.addAll(y);
        return x;
    };

    static Function<Pair<Long, Queue<Integer>>, Long> GET_FIRST = (x) -> (x.first);
    static Comparator<Pair<Long, Queue<Integer>>> C = Comparator.comparing(GET_FIRST);

    public static void main(String[] args) throws Exception {
        long startTime = System.nanoTime();
        int t = 1;
        while (t-- > 0) {
            solve();
        }
        long endTime = System.nanoTime();
        err.println("Execution Time : +" + (endTime - startTime) / 1000000 + " ms");
        exit(0);
    }

    static void solve() {
        long n = in.nextLong();
        int m = in.nextInt();
        long k = in.nextLong();
        long[] data = in.readAllLongs(m);
        Queue<Long> values = new ArrayDeque<>();
        for (int i = 0; i < m; i++) {
            values.add(data[i]);
        }
        int offset = 0;
        int ans = 0;
        while (true) {
            if (values.isEmpty()) {
                break;
            }
            long v = values.peek();
            long bucket = (v - offset + k - 1) / k;
            offset += process(values, bucket, offset, k);
            ans++;
        }
        out.println(ans);
    }

    static int process(Queue<Long> values, long bucket, int offSet, long k) {
        int ans = 0;
        while (!values.isEmpty()) {
            long v = values.peek();
            long b = (v - offSet + k - 1) / k;
            if (b == bucket) {
                ans++;
                values.poll();
            } else {
                break;
            }
        }
        return ans;
    }

    static void debug(Object... args) {
        for (Object a : args) {
            out.println(a);
        }
    }

    static void y() {
        out.println("YES");
    }

    static void n() {
        out.println("NO");
    }

    static <T> T min(T a, T b, Comparator<T> C) {
        if (C.compare(a, b) <= 0) {
            return a;
        }
        return b;
    }

    static <T> T max(T a, T b, Comparator<T> C) {
        if (C.compare(a, b) >= 0) {
            return a;
        }
        return b;
    }

    static void fail() {
        out.println("-1");
    }

    static class Pair<T, R> {
        public T first;
        public R second;

        public Pair(T first, R second) {
            this.first = first;
            this.second = second;
        }

        @Override
        public boolean equals(final Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }
            final Pair<?, ?> pair = (Pair<?, ?>) o;
            return Objects.equals(first, pair.first) && Objects.equals(second, pair.second);
        }

        @Override
        public int hashCode() {
            return Objects.hash(first, second);
        }

        @Override
        public String toString() {
            return "Pair{" + "a=" + first + ", b=" + second + '}';
        }

        public T getFirst() {
            return first;
        }

        public R getSecond() {
            return second;
        }
    }

    static <T, R> Pair<T, R> make_pair(T a, R b) {
        return new Pair<>(a, b);
    }

    static class ArrayUtils {

        static void swap(int[] a, int i, int j) {
            int temp = a[i];
            a[i] = a[j];
            a[j] = temp;
        }

        static void swap(char[] a, int i, int j) {
            char temp = a[i];
            a[i] = a[j];
            a[j] = temp;
        }

        static void print(char[] a) {
            for (char c : a) {
                out.print(c);
            }
            out.println("");
        }

        static int[] reverse(int[] data) {
            int[] p = new int[data.length];
            for (int i = 0, j = data.length - 1; i < data.length; i++, j--) {
                p[i] = data[j];
            }
            return p;
        }

        static void prefixSum(long[] data) {
            for (int i = 1; i < data.length; i++) {
                data[i] += data[i - 1];
            }
        }

        static void prefixSum(int[] data) {
            for (int i = 1; i < data.length; i++) {
                data[i] += data[i - 1];
            }
        }

        static long[] reverse(long[] data) {
            long[] p = new long[data.length];
            for (int i = 0, j = data.length - 1; i < data.length; i++, j--) {
                p[i] = data[j];
            }
            return p;
        }

        static char[] reverse(char[] data) {
            char[] p = new char[data.length];
            for (int i = 0, j = data.length - 1; i < data.length; i++, j--) {
                p[i] = data[j];
            }
            return p;
        }

        static int[] MergeSort(int[] A) {
            if (A.length > 1) {
                int q = A.length / 2;
                int[] left = new int[q];
                int[] right = new int[A.length - q];
                System.arraycopy(A, 0, left, 0, q);
                System.arraycopy(A, q, right, 0, A.length - q);
                int[] left_sorted = MergeSort(left);
                int[] right_sorted = MergeSort(right);
                return Merge(left_sorted, right_sorted);
            } else {
                return A;
            }
        }

        static int[] Merge(int[] left, int[] right) {
            int[] A = new int[left.length + right.length];
            int i = 0;
            int j = 0;
            for (int k = 0; k < A.length; k++) {
                // To handle left becoming empty
                if (i == left.length && j < right.length) {
                    A[k] = right[j];
                    j++;
                    continue;
                }
                // To handle right becoming empty
                if (j == right.length && i < left.length) {
                    A[k] = left[i];
                    i++;
                    continue;
                }
                if (left[i] <= right[j]) {
                    A[k] = left[i];
                    i++;
                } else {
                    A[k] = right[j];
                    j++;
                }
            }
            return A;
        }

        static long[] MergeSort(long[] A) {
            if (A.length > 1) {
                int q = A.length / 2;
                long[] left = new long[q];
                long[] right = new long[A.length - q];
                System.arraycopy(A, 0, left, 0, q);
                System.arraycopy(A, q, right, 0, A.length - q);
                long[] left_sorted = MergeSort(left);
                long[] right_sorted = MergeSort(right);
                return Merge(left_sorted, right_sorted);
            } else {
                return A;
            }
        }

        static long[] Merge(long[] left, long[] right) {
            long[] A = new long[left.length + right.length];
            int i = 0;
            int j = 0;
            for (int k = 0; k < A.length; k++) {
                // To handle left becoming empty
                if (i == left.length && j < right.length) {
                    A[k] = right[j];
                    j++;
                    continue;
                }
                // To handle right becoming empty
                if (j == right.length && i < left.length) {
                    A[k] = left[i];
                    i++;
                    continue;
                }
                if (left[i] <= right[j]) {
                    A[k] = left[i];
                    i++;
                } else {
                    A[k] = right[j];
                    j++;
                }
            }
            return A;
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 2048);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public int[] readAllInts(int n) {
            int[] p = new int[n];
            for (int i = 0; i < n; i++) {
                p[i] = in.nextInt();
            }
            return p;
        }

        public int[] readAllInts(int n, int s) {
            int[] p = new int[n + s];
            for (int i = s; i < n + s; i++) {
                p[i] = in.nextInt();
            }
            return p;
        }

        public long[] readAllLongs(int n) {
            long[] p = new long[n];
            for (int i = 0; i < n; i++) {
                p[i] = in.nextLong();
            }
            return p;
        }

        public long[] readAllLongs(int n, int s) {
            long[] p = new long[n + s];
            for (int i = s; i < n + s; i++) {
                p[i] = in.nextLong();
            }
            return p;
        }

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

    static void exit(int a) {
        out.close();
        err.close();
        System.exit(a);
    }

    static InputStream inputStream = System.in;
    static OutputStream outputStream = System.out;
    static OutputStream errStream = System.err;
    static InputReader in = new InputReader(inputStream);
    static PrintWriter out = new PrintWriter(outputStream);
    static PrintWriter err = new PrintWriter(errStream);
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

}
