Mr. Bender has a digital table of size n × n, each cell can be switched on or off. He wants the field to have at least c switched on squares. When this condition is fulfilled, Mr Bender will be happy.

We'll consider the table rows numbered from top to bottom from 1 to n, and the columns — numbered from left to right from 1 to n. Initially there is exactly one switched on cell with coordinates (x, y) (x is the row number, y is the column number), and all other cells are switched off. Then each second we switch on the cells that are off but have the side-adjacent cells that are on.

For a cell with coordinates (x, y) the side-adjacent cells are cells with coordinates (x - 1, y), (x + 1, y), (x, y - 1), (x, y + 1).

In how many seconds will Mr. Bender get happy?

Input

The first line contains four space-separated integers n, x, y, c (1 ≤ n, c ≤ 109; 1 ≤ x, y ≤ n; c ≤ n2).

Output

In a single line print a single integer — the answer to the problem.

Examples

Input

6 4 3 1


Output

0


Input

9 3 8 10


Output

2

Note

Initially the first test has one painted cell, so the answer is 0. In the second test all events will go as is shown on the figure. <image>.
import javafx.util.Pair;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {

    IIO io;

    Main(IIO io) {
        this.io = io;
    }

    public static void main(String[] args) throws IOException {

        ConsoleIO io = new ConsoleIO();
        Main m = new Main(io);
        m.solve();
        io.flush();

//        Tester test = new Tester();test.run();
    }



    public void solve() {
        int[] l = io.readIntArray();
        int n = l[0], x = l[1], y = l[2], c = l[3];
        c--;
        int res = 0;
        int x1 = x-1;
        int xn = n-x;
        int y1 = y -1;
        int yn = n-y;

        int q1 = 0, q2 = 0, q3 = 0, q4 = 0;

        for (int d = 1; c > 0; d++, res++) {

            if(d<=x1+1 && d<=y1)q2++;
            else if(d>x1+1 && d>y1)q2 = Math.max(0,q2-1);

            if(d<=x1 && d<=yn + 1)q3++;
            else if(d>x1 && d>yn+1)q3 = Math.max(0,q3-1);

            if(d<=xn && d<=y1+1)q1++;
            else if(d>xn && d>y1+1)q1 = Math.max(0,q1-1);

            if(d<=xn+1 && d<=yn)q4++;
            else if(d>xn+1 && d>yn)q4 = Math.max(0,q4-1);

            c-=q1+q2+q3+q4;
        }
        io.writeLine(Integer.toString(res));
    }


}

class ConsoleIO extends BaseIO {
    BufferedReader br;
    PrintWriter out;
    public ConsoleIO(){
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
    }
    public void flush(){
        this.out.close();
    }
    public void writeLine(String s) {
        this.out.println(s);
    }
    public void writeInt(int a) {
        this.out.print(a);
        this.out.print(' ');
    }
    public void writeWord(String s){
        this.out.print(s);
    }
    public String readLine() {
        try {
            return br.readLine();
        }
        catch (Exception ex){
            return "";
        }
    }
    public int read(){
        try {
            return br.read();
        }
        catch (Exception ex){
            return -1;
        }
    }
}
abstract class BaseIO implements IIO {

    public long readLong() {
        return Long.parseLong(this.readLine());
    }

    public int readInt() {
        return Integer.parseInt(this.readLine());
    }

    public int[] readIntArray() {
        String line = this.readLine();
        String[] nums = line.split(" ");
        int[] res = new int[nums.length];
        for (int i = 0; i < nums.length; i++) {
            res[i] = Integer.parseInt(nums[i]);
        }
        return res;
    }
    public long[] readLongArray() {
        String line = this.readLine();
        String[] nums = line.split(" ");
        long[] res = new long[nums.length];
        for (int i = 0; i < nums.length; i++) {
            res[i] = Long.parseLong(nums[i]);
        }
        return res;
    }
}
interface IIO {
    void writeLine(String s);
    void writeInt(int a);
    void writeWord(String s);
    String readLine();
    long readLong();
    int readInt();
    int read();
    int[] readIntArray();
    long[] readLongArray();
}

