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.BufferedReader;
import java.io.File;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class MrBenderAndSquare {

	public static void main(String[] args) throws IOException {
		MyScanner sc = new MyScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		long n = sc.nextLong(), x = sc.nextLong(), y = sc.nextLong(), c = sc.nextLong();
		long low = 0, high = (long) 1e5, ans = 0;
		while (low <= high) {
			long mid = (low + high) >> 1, cells = 0;
			for (long i = y; i <= n && i <= y + mid; i++) {
				long up = x - mid + (i - y), down = x + mid - (i - y);
				up = Math.max(up, 1);
				down = Math.min(down, n);
				cells += down - up + 1;
			}
			for (long i = y - 1; i >= 1 && i >= y - mid; i--) {
				long up = x - mid + (y - i), down = x + mid - (y - i);
				up = Math.max(up, 1);
				down = Math.min(down, n);
				cells += down - up + 1;
			}
			if (cells < c) {
				low = mid + 1;
			} else {
				high = mid - 1;
				ans = mid;
			}
		}
		out.println(ans);
		out.flush();
		out.close();
	}

	static class MyScanner {

		BufferedReader br;
		StringTokenizer st;

		MyScanner(InputStream is) {
			br = new BufferedReader(new InputStreamReader(is));
		}

		MyScanner(String filename) throws IOException {
			br = new BufferedReader(new FileReader(new File(filename)));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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