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 java.io.*;
import java.util.*;

public class P255D
{
    public static StringTokenizer st;
    public static void nextLine(BufferedReader br) throws IOException
    {
        st = new StringTokenizer(br.readLine());
    }
    
    public static String next()
    {
        return st.nextToken();
    }
    
    public static int nextInt()
    {
        return Integer.parseInt(st.nextToken());
    }
    
    public static long nextLong()
    {
        return Long.parseLong(st.nextToken());
    }
    
    public static void main(String[] args) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        nextLine(br);
        long n = nextLong();
        long x = nextLong();
        long y = nextLong();
        long c = nextLong();
        long min = 0;
        long max = 2*n;
        while (min < max)
        {
            long mid = (min + max) / 2;
            long cells = calc(n, x, y, mid);
            if (cells < c)
            {
                min = mid+1;
            }
            else
            {
                max = mid;
            }
        }
        System.out.println(min);
    }
    
    private static long calc(long n, long x, long y, long m)
    {
        long base = 1 + 2 * m * (m+1);
        if (x - m < 1)
        {
            long d = m-x+1;
            long bd = d*d;
            base -= bd;
        }
        if (y - m < 1)
        {
            long d = m-y+1;
            long bd = d*d;
            base -= bd;
        }
        if (x + m > n)
        {
            long d = x+m-n;
            long bd = d*d;
            base -= bd;
        }
        if (y + m > n)
        {
            long d = y+m-n;
            long bd = d*d;
            base -= bd;
        }
        if (x + y - m < 1)
        {
            long d = 1 + m - x - y;
            long bd = (d * (d+1)) / 2;
            base += bd;
        }
        if (x + (n-y) < m)
        {
            long d = m - (x + n - y);
            long bd = (d * (d+1)) / 2;
            base += bd;
        }
        if (x + y + m > 2*n+1)
        {
            long d = (x+y+m) - (2*n+1);
            long bd = (d * (d+1)) / 2;
            base += bd;
        }
        if (y + (n-x) < m)
        {
            long d = m - (y + n - x);
            long bd = (d * (d+1)) / 2;
            base += bd;
        }
        return base;
    }
}
