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 sys
text = raw_input()
param  = text.split()
n=int(param[0])
x=int(param[1])
y=int(param[2])
c=int(param[3])
if (c==1):
	print 0
else:
	cur = 1
	step = 0
	top = y
	left = x
	right = x
	bottom = y
	counts = 0	
	while (cur < c):
		step = step +1
		counts = 0
		flag_count = 0; 
		top = top -1
		left = left -1
		right = right +1
		bottom = bottom +1

		if (top < 1):
			None
		else:
			flag_count = flag_count +1

		if (right > n):
			None
		else:
			flag_count = flag_count +1

		if (bottom > n):
			None
		else:
			flag_count = flag_count +1

		if (left < 1):
			None
		else:
			flag_count = flag_count +1

		counts = counts + max(step +1  - max((1 - top), 0) - max(right - n, 0), 0)
		counts = counts + max(step +1  - max((1 - top), 0) - max(1 - left, 0), 0)
		counts = counts + max(step +1  - max((bottom - n), 0) - max(1 - left, 0), 0)
		counts = counts + max(step +1  - max((bottom - n), 0) - max(right - n, 0), 0)

		# print counts
		counts = counts - flag_count
		cur = cur + counts;
		# print counts
	print step 