Mr. Bender and Square

2000ms

262144K

Description:

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?

Input:

The first line contains four space-separated integers n, x, y, c (1 ≤ n, c ≤ 10⁹; 1 ≤ x, y ≤ n; c ≤ n²).

Output:

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

Sample Input:

6 4 3 1

Sample Output:

Sample Input:

9 3 8 10

Sample Output:

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. $\text{[math]}$ .

Informação

Provedor Codeforces

Código CF255D