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. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF255D/b709c1aa5b91b7af907cf3f3ca10b895a1b76650.png).