CF255D.Mr. Bender and Square

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?

本德先生有一块大小为 $n \times n$ 的数字表格，每个格子可以开启或关闭。他希望表格中至少有 $c$ 个开启的格子；当这一条件满足时，本德先生就会感到开心。

我们将表格的行从上到下编号为 $1$ 到 $n$，列从左到右编号为 $1$ 到 $n$。初始时刻，恰好有一个格子处于开启状态，其坐标为 $(x, y)$（其中 $x$ 为行号，$y$ 为列号），其余所有格子均处于关闭状态。此后，每一秒，我们都会将所有当前处于关闭状态、但具有边相邻（即共享一条边）的开启格子的格子开启。

对于坐标为 $(x, y)$ 的格子，其边相邻格子的坐标分别为 $(x-1, y)$、$(x+1, y)$、$(x, y-1)$ 和 $(x, y+1)$。

请问：本德先生需要多少秒才会开心？

The first line contains four space-separated integers n, x, y, c (1 ≤ n, c ≤ 109; 1 ≤ x, y ≤ n; c ≤ _n_2).

第一行包含四个以空格分隔的整数 $n$、$x$、$y$、$c$（$1 \le n, c \le 10^9$；$1 \le x, y \le n$；$c \le n^2$）。

In a single line print a single integer — the answer to the problem.

在一行中输出一个整数——该问题的答案。

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. .

最初，第一次测试中只有一个被涂色的单元格，因此答案为 0。在第二次测试中，所有事件的发生过程如图所示。