#include <bits/stdc++.h>
using namespace std;
int n;
int x, y;
long long total(long long t) {
  if (!t) return 1;
  return 1 + 2 * t * t + 2 * t;
}
long long soma(long long meio) {
  if (meio <= 0) return 0;
  return (1 + meio) * meio - meio;
}
long long dist(long long a, long long b) { return abs(a - x) + abs(b - y); }
long long getFolga(long long a, long long b, long long t) {
  long long d = dist(a, b), folga = t - d + 1;
  if (folga <= t && folga > 0) return ((1 + folga) * folga) / 2;
  return 0;
}
long long getArea(long long t) {
  long long area = total(t);
  if (0) cout << "Area " << area << endl;
  area -= soma(x + t - n + 1);
  if (0) cout << "1: " << soma(x + t - n + 1) << endl;
  area -= soma(y + t - n + 1);
  if (0) cout << "2: " << soma(y + t - n + 1) << endl;
  area -= soma(-(x - t));
  if (0) cout << "3: " << soma(-(x - t)) << endl;
  area -= soma(-(y - t));
  if (0) cout << "4: " << soma(-(y - t)) << endl;
  area += getFolga(-1, -1, t);
  if (0) cout << "5: " << getFolga(-1, -1, t) << endl;
  area += getFolga(n, n, t);
  if (0) cout << "6: " << getFolga(n, n, t) << endl;
  area += getFolga(-1, n, t);
  if (0) cout << "7: " << getFolga(-1, n, t) << endl;
  area += getFolga(n, -1, t);
  if (0) cout << "8: " << getFolga(n, -1, t) << endl;
  return area;
}
int main() {
  long long c;
  cin >> n >> x >> y >> c;
  --x;
  --y;
  long long ini = 0, fim = 2000000000LL, resp = -1;
  if (0) cout << getArea(3) << endl;
  while (ini <= fim) {
    long long t = (ini + fim) / 2;
    long long area = getArea(t);
    if (area >= c) {
      resp = t;
      fim = t - 1;
    } else
      ini = t + 1;
  }
  cout << resp << endl;
}

### Prompt

Please create a solution in cpp 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;
int n;
int x, y;
long long total(long long t) {
  if (!t) return 1;
  return 1 + 2 * t * t + 2 * t;
}
long long soma(long long meio) {
  if (meio <= 0) return 0;
  return (1 + meio) * meio - meio;
}
long long dist(long long a, long long b) { return abs(a - x) + abs(b - y); }
long long getFolga(long long a, long long b, long long t) {
  long long d = dist(a, b), folga = t - d + 1;
  if (folga <= t && folga > 0) return ((1 + folga) * folga) / 2;
  return 0;
}
long long getArea(long long t) {
  long long area = total(t);
  if (0) cout << "Area " << area << endl;
  area -= soma(x + t - n + 1);
  if (0) cout << "1: " << soma(x + t - n + 1) << endl;
  area -= soma(y + t - n + 1);
  if (0) cout << "2: " << soma(y + t - n + 1) << endl;
  area -= soma(-(x - t));
  if (0) cout << "3: " << soma(-(x - t)) << endl;
  area -= soma(-(y - t));
  if (0) cout << "4: " << soma(-(y - t)) << endl;
  area += getFolga(-1, -1, t);
  if (0) cout << "5: " << getFolga(-1, -1, t) << endl;
  area += getFolga(n, n, t);
  if (0) cout << "6: " << getFolga(n, n, t) << endl;
  area += getFolga(-1, n, t);
  if (0) cout << "7: " << getFolga(-1, n, t) << endl;
  area += getFolga(n, -1, t);
  if (0) cout << "8: " << getFolga(n, -1, t) << endl;
  return area;
}
int main() {
  long long c;
  cin >> n >> x >> y >> c;
  --x;
  --y;
  long long ini = 0, fim = 2000000000LL, resp = -1;
  if (0) cout << getArea(3) << endl;
  while (ini <= fim) {
    long long t = (ini + fim) / 2;
    long long area = getArea(t);
    if (area >= c) {
      resp = t;
      fim = t - 1;
    } else
      ini = t + 1;
  }
  cout << resp << endl;
}

```