Mr. Bender and Square

题意翻译

给定一个n*n的正方形，给出（x，y）的点，每秒 可以向外扩散（x+1,y） (x-1,y) (x,y+1) (x,y-1),求需要多少秒才能大于或等于面积C

题目描述

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?

输入输出格式

输入格式

The first line contains four space-separated integers $ n,x,y,c $ $ (1<=n,c<=10^{9}; 1<=x,y<=n; c<=n^{2}) $ .

输出格式

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

输入输出样例

输入样例 #1

6 4 3 1

输出样例 #1

0

输入样例 #2

9 3 8 10

输出样例 #2

2

说明

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. .