A8820 | Mr. Bender and Square

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 $n,x,y,c$ $(1<=n,c<=10^{9}; 1<=x,y<=n; c<=n^{2})$ .

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