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

def subArea(x, y, step):
    step += 1
    x, y = sorted([x, y])
    if step <= x:
        return step * (step + 1) / 2
    if step <= y:
        return x * (x + 1) / 2 + (step - x) * x
    if step <= x + y:
        return x * (x + 1) / 2 + (y - x) * x + (x * (x - 1) - (x + y - step) * (x + y - step - 1)) / 2
    return x * y

def area(n, x, y, step):
    result = subArea(x, y, step) + subArea(n - x + 1, y, step) + subArea(x, n - y + 1, step) + subArea(n - x + 1, n - y +1, step)
    result -= min(x, step + 1) + min(n - x + 1, step + 1) + min(y, step + 1) + min(n - y + 1, step + 1)
    result += 1
    return result

def findMinStep(n, x, y, c):
    if c <= 1:
        return 0

    left, right = 0, 2 * n
    middle = (left + right) / 2
    while not (area(n, x, y, middle + 1) >= c and area(n, x, y, middle) < c):
        if area(n, x, y, middle + 1) >= c:
            right = middle
        else:
            left = middle
        middle = (left + right) / 2
    return middle + 1

def main():
    n, x, y, c = map(int, raw_input().split())
    print findMinStep(n, x, y, c)

if __name__ == '__main__':
    main()
