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.

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. <image>.
#include <bits/stdc++.h>
using namespace std;
long long n, x, y, c;
long long cont(long long t) {
  long long cnt = t * (2 * t + 2) + 1, out, az;
  out = x + t - n;
  if (out > 0) cnt -= out * out;
  out = -(x - t - 1);
  if (out > 0) cnt -= out * out;
  out = y + t - n;
  if (out > 0) {
    az = max(0ll, out - (n - x));
    cnt -= (az + out) * (out - az + 1) / 2;
    out--;
    az = max(0ll, out - x + 2);
    cnt -= (az + out) * (out - az + 1) / 2;
  }
  out = -(y - t - 1);
  if (out > 0) {
    az = max(0ll, out - (n - x));
    cnt -= (az + out) * (out - az + 1) / 2;
    out--;
    az = max(0ll, out - x + 2);
    cnt -= (az + out) * (out - az + 1) / 2;
  }
  return cnt;
}
int main() {
  scanf("%I64d%I64d%I64d%I64d", &n, &x, &y, &c);
  long long lb = -1, rb = 2010000000;
  while (lb != rb - 1) {
    long long mid = (lb + rb) / 2;
    if (cont(mid) >= c)
      rb = mid;
    else
      lb = mid;
  }
  printf("%I64d\n", rb);
}
