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.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		long x = sc.nextLong();
		long y = sc.nextLong();
		long c = sc.nextLong();

		long top = x;
		long bot = x;
		long left = y;
		long right = y;
		
		long topoutadd=1;
		long botoutadd=1;
		long leftoutadd=1;
		long rightoutadd=1;
		
		long topoutright=y;
		long topoutleft=y;
		long botoutright=y;
		long botoutleft=y;

		long add = 4;

		long tot = 1;
		long sec = 0;
		
		int removetopfromright=0;
		int removetopfromleft=0;
		int removebotformright=0;
		int removebotfromleft=0;
		
		
		while (tot < c) {
			sec++;
			bot++;
			top--;
			right++;
			left--;

			tot += add;
			
			if (top <= 0) {
				
				if(top<0) {
				topoutright++;
				topoutleft--;
					if(topoutright>n) {
						removetopfromright++;
						tot+=removetopfromright;
					}
					
					if(topoutleft<=0) {
						removetopfromleft++;
						tot+=removetopfromleft;
					}
				}
				
				tot-=topoutadd;
				topoutadd+=2;
			}
			
			if (bot > n) {
				
				if(bot>n+1) {
					
				botoutright++;
				botoutleft--;
					if(botoutright>n) {
						removebotformright++;
						tot+=removebotformright;
					}
					
					if(botoutleft<=0) {
						removebotfromleft++;
						tot+=removebotfromleft;
					}
				}
				
				tot-=botoutadd;
				botoutadd+=2;
			}
			if (right > n) {
				tot-=rightoutadd;
				rightoutadd+=2;
			}
			if (left <=0) {
				tot-=leftoutadd;
				leftoutadd+=2;
			}
			
			add+=4;
			
		}
		System.out.println(sec);
		

	}

}
