Vanya smashes potato in a vertical food processor. At each moment of time the height of the potato in the processor doesn't exceed h and the processor smashes k centimeters of potato each second. If there are less than k centimeters remaining, than during this second processor smashes all the remaining potato.

Vanya has n pieces of potato, the height of the i-th piece is equal to ai. He puts them in the food processor one by one starting from the piece number 1 and finishing with piece number n. Formally, each second the following happens:

  1. If there is at least one piece of potato remaining, Vanya puts them in the processor one by one, until there is not enough space for the next piece. 
  2. Processor smashes k centimeters of potato (or just everything that is inside). 



Provided the information about the parameter of the food processor and the size of each potato in a row, compute how long will it take for all the potato to become smashed.

Input

The first line of the input contains integers n, h and k (1 ≤ n ≤ 100 000, 1 ≤ k ≤ h ≤ 109) — the number of pieces of potato, the height of the food processor and the amount of potato being smashed each second, respectively.

The second line contains n integers ai (1 ≤ ai ≤ h) — the heights of the pieces.

Output

Print a single integer — the number of seconds required to smash all the potatoes following the process described in the problem statement.

Examples

Input

5 6 3
5 4 3 2 1


Output

5


Input

5 6 3
5 5 5 5 5


Output

10


Input

5 6 3
1 2 1 1 1


Output

2

Note

Consider the first sample. 

  1. First Vanya puts the piece of potato of height 5 into processor. At the end of the second there is only amount of height 2 remaining inside. 
  2. Now Vanya puts the piece of potato of height 4. At the end of the second there is amount of height 3 remaining. 
  3. Vanya puts the piece of height 3 inside and again there are only 3 centimeters remaining at the end of this second. 
  4. Vanya finally puts the pieces of height 2 and 1 inside. At the end of the second the height of potato in the processor is equal to 3. 
  5. During this second processor finally smashes all the remaining potato and the process finishes. 



In the second sample, Vanya puts the piece of height 5 inside and waits for 2 seconds while it is completely smashed. Then he repeats the same process for 4 other pieces. The total time is equal to 2·5 = 10 seconds.

In the third sample, Vanya simply puts all the potato inside the processor and waits 2 seconds.
//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 h = io.nextInt();
        int k = io.nextInt();
        int[] a = new int[n+1];
        long time = 0L;
        long curr = 0L;
        for (int i=1; i<=n; i++) {
            a[i] = io.nextInt();
            if (curr + a[i] > h) {
                long chop = curr / k;
                curr -= (k * chop);
                time += chop;
            }
            if (curr + a[i] > h) {
                time += 1;
                curr = 0;
            }
            curr += a[i];
        }

        long chop = curr / k;
        curr -= (k * chop);
        time += chop;
        if (curr > 0) {
            time += 1;
            curr = 0;
        }
        System.out.println(time);
    }

    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());
    }

}