Problem Mr. Bender and Square

Link: http://codeforces.com/problemset/problem/255/D

D. Mr. Bender and Square

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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 test(s)

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..

Thuật toán:
Để giải quyết bài toán trên, chúng ta giải bài toán con sau.
Chúng ta cần tính số ô chúng ta có được khi xuất phát từ ô (x, y) sau t bước.
Chúng ta gọi đó là hàm f(x,y,t).