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>
template <typename T>
void read(T& val) {
  std::string tmp = typeid(val).name();
  if (strcmp(tmp.c_str(), "i") == 0)
    scanf("%d", &val);
  else if (strcmp(tmp.c_str(), "x") == 0)
    scanf("%I64d", &val);
  else if (strcmp(tmp.c_str(), "d") == 0)
    scanf("%lf", &val);
  else if (tmp.length() > 2 && tmp.back() == 'c')
    scanf("%s", val);
  else if (strcmp(tmp.c_str(), "c") == 0)
    scanf("%c", &val);
}
template <typename T, typename... Targs>
void read(T& val, Targs&... Fargs) {
  read(val);
  read(Fargs...);
}
template <typename T>
void print(T val) {
  std::string tmp = typeid(val).name();
  if (strcmp(tmp.c_str(), "i") == 0)
    printf("%d", val);
  else if (strcmp(tmp.c_str(), "x") == 0)
    printf("%I64d", val);
  else if (strcmp(tmp.c_str(), "d") == 0)
    printf("%.15f", val);
  else if (strcmp(tmp.c_str(), "c") == 0)
    printf("%c", val);
  else if (tmp.length() > 2 && tmp.back() == 'c')
    printf("%s", val);
}
template <typename T, typename... Targs>
void print(T val, Targs... Fargs) {
  print(val);
  print(Fargs...);
}
const double pi = acos(-1);
const int MOD = 1e9 + 7;
const int INF = 1e9 + 7;
const int MAXN = 1e6 + 5;
const double eps = 1e-9;
using namespace std;
int a = 1, b, c, n, x, y, z;
int main() {
  read(n, x, y, c);
  while (a < c) {
    b++;
    z = min(x - 1, b);
    a += max(z - max((y + b - n), 0) + 1, 0) +
         max(z - max((b - y + 1), 0) + 1, 0) - (z == b);
    z = min(n - x, b);
    a += max(z - max((y + b - n), 1) + 1, 0) +
         max(z - max((b - y + 1), 1) + 1, 0) - (z == b);
  }
  print(b);
  return 0;
}
