#include <bits/stdc++.h>
using namespace std;
long long x, y, n, c;
long long tri(long long n) { return n * (n + 1) / 2; }
long long make(long long s) {
  long long ans = 1;
  if (s == 0) return ans;
  if (x - s > 0)
    ans = ans + s;
  else
    ans = ans + x - 1;
  if (x + s <= n)
    ans = ans + s;
  else
    ans = ans + n - x;
  if (y - s > 0)
    ans = ans + s;
  else
    ans = ans + y - 1;
  if (y + s <= n)
    ans = ans + s;
  else
    ans = ans + n - y;
  if (s == 1) return ans;
  long long xx, yy, ss;
  xx = x - 1;
  yy = y - 1;
  ss = s - 1;
  if (xx - ss + 1 > 0 && yy - ss + 1 > 0) {
    ans = ans + tri(ss);
  }
  if (xx - ss + 1 <= 0 && yy - ss + 1 > 0) {
    ans = ans + tri(ss) - tri(ss - xx);
  }
  if (xx - ss + 1 > 0 && yy - ss + 1 <= 0) {
    ans = ans + tri(ss) - tri(ss - yy);
  }
  if (xx - ss + 1 < 0 && yy - ss + 1 <= 0) {
    if (ss >= xx + yy - 1)
      ans = ans + xx * yy;
    else
      ans = ans + tri(ss) - tri(ss - xx) - tri(ss - yy);
  }
  xx = x + 1;
  yy = y - 1;
  if (xx + ss - 1 <= n && yy - ss + 1 > 0) {
    ans = ans + tri(ss);
  }
  if (xx + ss - 1 > n && yy - ss + 1 > 0) {
    ans = ans + tri(ss) - tri(xx + ss - 1 - n);
  }
  if (xx + ss - 1 <= n && yy - ss + 1 <= 0) {
    ans = ans + tri(ss) - tri(ss - yy);
  }
  if (xx + ss - 1 > n && yy - ss + 1 <= 0) {
    if (ss >= n - xx + yy)
      ans = ans + (n - xx + 1) * yy;
    else
      ans = ans + tri(ss) - tri(xx + ss - 1 - n) - tri(ss - yy);
  }
  xx = x - 1;
  yy = y + 1;
  if (xx - ss + 1 > 0 && yy + ss - 1 <= n) ans = ans + tri(ss);
  if (xx - ss + 1 > 0 && yy + ss - 1 > n)
    ans = ans + tri(ss) - tri(yy + ss - 1 - n);
  if (xx - ss + 1 <= 0 && yy + ss - 1 <= n) ans = ans + tri(ss) - tri(ss - xx);
  if (xx - ss + 1 <= 0 && yy + ss - 1 > n) {
    if (ss >= n - yy + xx)
      ans = ans + xx * (n - yy + 1);
    else
      ans = ans + tri(ss) - tri(yy + ss - 1 - n) - tri(ss - xx);
  }
  xx = x + 1;
  yy = y + 1;
  if (xx + ss - 1 <= n && yy + ss - 1 <= n) ans = ans + tri(ss);
  if (xx + ss - 1 > n && yy + ss - 1 <= n)
    ans = ans + tri(ss) - tri(xx + ss - 1 - n);
  if (xx + ss - 1 <= n && yy + ss - 1 > n)
    ans = ans + tri(ss) - tri(yy + ss - 1 - n);
  if (xx + ss - 1 > n && yy + ss - 1 > n) {
    if (ss >= 2 * n - xx - yy + 1)
      ans = ans + (n - xx + 1) * (n - yy + 1);
    else
      ans = ans + tri(ss) - tri(xx + ss - 1 - n) - tri(yy + ss - 1 - n);
  }
  return ans;
}
int main() {
  scanf("%lld%lld%lld%lld", &n, &x, &y, &c);
  long long l, r;
  l = 0;
  r = n * 3;
  while (l < r) {
    long long mid = (l + r) / 2;
    long long temp = make(mid);
    if (temp >= c)
      r = mid;
    else
      l = mid + 1;
  }
  printf("%lld\n", l);
}

### Prompt

Generate a CPP solution to the following problem:

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>.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long x, y, n, c;
long long tri(long long n) { return n * (n + 1) / 2; }
long long make(long long s) {
  long long ans = 1;
  if (s == 0) return ans;
  if (x - s > 0)
    ans = ans + s;
  else
    ans = ans + x - 1;
  if (x + s <= n)
    ans = ans + s;
  else
    ans = ans + n - x;
  if (y - s > 0)
    ans = ans + s;
  else
    ans = ans + y - 1;
  if (y + s <= n)
    ans = ans + s;
  else
    ans = ans + n - y;
  if (s == 1) return ans;
  long long xx, yy, ss;
  xx = x - 1;
  yy = y - 1;
  ss = s - 1;
  if (xx - ss + 1 > 0 && yy - ss + 1 > 0) {
    ans = ans + tri(ss);
  }
  if (xx - ss + 1 <= 0 && yy - ss + 1 > 0) {
    ans = ans + tri(ss) - tri(ss - xx);
  }
  if (xx - ss + 1 > 0 && yy - ss + 1 <= 0) {
    ans = ans + tri(ss) - tri(ss - yy);
  }
  if (xx - ss + 1 < 0 && yy - ss + 1 <= 0) {
    if (ss >= xx + yy - 1)
      ans = ans + xx * yy;
    else
      ans = ans + tri(ss) - tri(ss - xx) - tri(ss - yy);
  }
  xx = x + 1;
  yy = y - 1;
  if (xx + ss - 1 <= n && yy - ss + 1 > 0) {
    ans = ans + tri(ss);
  }
  if (xx + ss - 1 > n && yy - ss + 1 > 0) {
    ans = ans + tri(ss) - tri(xx + ss - 1 - n);
  }
  if (xx + ss - 1 <= n && yy - ss + 1 <= 0) {
    ans = ans + tri(ss) - tri(ss - yy);
  }
  if (xx + ss - 1 > n && yy - ss + 1 <= 0) {
    if (ss >= n - xx + yy)
      ans = ans + (n - xx + 1) * yy;
    else
      ans = ans + tri(ss) - tri(xx + ss - 1 - n) - tri(ss - yy);
  }
  xx = x - 1;
  yy = y + 1;
  if (xx - ss + 1 > 0 && yy + ss - 1 <= n) ans = ans + tri(ss);
  if (xx - ss + 1 > 0 && yy + ss - 1 > n)
    ans = ans + tri(ss) - tri(yy + ss - 1 - n);
  if (xx - ss + 1 <= 0 && yy + ss - 1 <= n) ans = ans + tri(ss) - tri(ss - xx);
  if (xx - ss + 1 <= 0 && yy + ss - 1 > n) {
    if (ss >= n - yy + xx)
      ans = ans + xx * (n - yy + 1);
    else
      ans = ans + tri(ss) - tri(yy + ss - 1 - n) - tri(ss - xx);
  }
  xx = x + 1;
  yy = y + 1;
  if (xx + ss - 1 <= n && yy + ss - 1 <= n) ans = ans + tri(ss);
  if (xx + ss - 1 > n && yy + ss - 1 <= n)
    ans = ans + tri(ss) - tri(xx + ss - 1 - n);
  if (xx + ss - 1 <= n && yy + ss - 1 > n)
    ans = ans + tri(ss) - tri(yy + ss - 1 - n);
  if (xx + ss - 1 > n && yy + ss - 1 > n) {
    if (ss >= 2 * n - xx - yy + 1)
      ans = ans + (n - xx + 1) * (n - yy + 1);
    else
      ans = ans + tri(ss) - tri(xx + ss - 1 - n) - tri(yy + ss - 1 - n);
  }
  return ans;
}
int main() {
  scanf("%lld%lld%lld%lld", &n, &x, &y, &c);
  long long l, r;
  l = 0;
  r = n * 3;
  while (l < r) {
    long long mid = (l + r) / 2;
    long long temp = make(mid);
    if (temp >= c)
      r = mid;
    else
      l = mid + 1;
  }
  printf("%lld\n", l);
}

```