6273: Mr
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?
The first line contains four space-separated integers n,x,y,c (1≤n,c≤109;1≤x,y≤n;c≤n2).
In a single line print a single integer − the answer to the problem.
6 4 3 1
0
9 3 8 10
2
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. 
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