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D. Mr. Bender and Square

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMr. 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* ≤ 10^{9}; 1 ≤ *x*, *y* ≤ *n*; *c* ≤ *n*^{2}).

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. .

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