#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
template <typename T, size_t N>
int SIZE(const T (&t)[N]) {
  return N;
}
template <typename T>
int SIZE(const T &t) {
  return t.size();
}
string to_string(const string s, int x1 = 0, int x2 = 1e9) {
  return '"' + ((x1 < s.size()) ? s.substr(x1, x2 - x1 + 1) : "") + '"';
}
string to_string(const char *s) { return to_string((string)s); }
string to_string(const bool b) { return (b ? "true" : "false"); }
string to_string(const char c) { return string({c}); }
template <size_t N>
string to_string(const bitset<N> &b, int x1 = 0, int x2 = 1e9) {
  string t = "";
  for (int __iii__ = min(x1, SIZE(b)), __jjj__ = min(x2, SIZE(b) - 1);
       __iii__ <= __jjj__; ++__iii__) {
    t += b[__iii__] + '0';
  }
  return '"' + t + '"';
}
template <typename A, typename... C>
string to_string(const A(&v), int x1 = 0, int x2 = 1e9, C... coords);
int l_v_l_v_l = 0, t_a_b_s = 0;
template <typename A, typename B>
string to_string(const pair<A, B> &p) {
  l_v_l_v_l++;
  string res = "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
  l_v_l_v_l--;
  return res;
}
template <typename A, typename... C>
string to_string(const A(&v), int x1, int x2, C... coords) {
  int rnk = rank<A>::value;
  string tab(t_a_b_s, ' ');
  string res = "";
  bool first = true;
  if (l_v_l_v_l == 0) res += '\n';
  res += tab + "[";
  x1 = min(x1, SIZE(v)), x2 = min(x2, SIZE(v));
  auto l = begin(v);
  advance(l, x1);
  auto r = l;
  advance(r, (x2 - x1) + (x2 < SIZE(v)));
  for (auto e = l; e != r; e = next(e)) {
    if (!first) {
      res += ", ";
    }
    first = false;
    l_v_l_v_l++;
    if (e != l) {
      if (rnk > 1) {
        res += '\n';
        t_a_b_s = l_v_l_v_l;
      };
    } else {
      t_a_b_s = 0;
    }
    res += to_string(*e, coords...);
    l_v_l_v_l--;
  }
  res += "]";
  if (l_v_l_v_l == 0) res += '\n';
  return res;
}
void dbgm() { ; }
template <typename Heads, typename... Tails>
void dbgm(Heads H, Tails... T) {
  cout << to_string(H) << " | ";
  dbgm(T...);
}
const long long MOD = (int)1e9 + 7;
string ascii_lowercase = "abcdefghijklmnopqrstuvwxyz";
string ascii_uppercase = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
long long inv(long long a, long long b) {
  return 1 < a ? b - inv(b % a, a) * b / a : 1;
}
const long long INF = 1e6;
unordered_map<int, int, custom_hash> mp;
long long gcd(long long a, long long b, long long &x, long long &y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  long long x1, y1;
  long long d = gcd(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
long long distsq(long long x1, long long y1, long long x2, long long y2) {
  return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
}
long long n, x, y, c;
long long topArea(long long t) {
  long long topTip = x - t;
  long long len = max(0LL, 0 - topTip + 1);
  return len * len;
}
long long leftArea(long long t) {
  long long leftTip = y - t;
  long long len = max(0LL, 0 - leftTip + 1);
  return len * len;
}
long long rightArea(long long t) {
  long long rightTip = y + t;
  long long len = max(0LL, rightTip - n);
  return len * len;
}
long long botArea(long long t) {
  long long botTip = x + t;
  long long len = max(0LL, botTip - n);
  return len * len;
}
long long topLeft(long long t) {
  long long dist = x + y;
  long long len = max(0LL, t - dist + 1);
  return len * (len + 1) / 2;
}
long long topRight(long long t) {
  long long dist = (n + 1) - y + x;
  long long len = max(0LL, t - dist + 1);
  return len * (len + 1) / 2;
}
long long botRight(long long t) {
  long long dist = (n + 1) - y + (n + 1) - x;
  long long len = max(0LL, t - dist + 1);
  return len * (len + 1) / 2;
}
long long botLeft(long long t) {
  long long dist = (n + 1) - x + y;
  long long len = max(0LL, t - dist + 1);
  return len * (len + 1) / 2;
}
long long getArea(long long t) {
  long long square = 2 * t * (t + 1) + 1;
  long long tp = topArea(t);
  long long bt = botArea(t);
  long long lt = leftArea(t);
  long long rt = rightArea(t);
  long long topleft = topLeft(t);
  long long topright = topRight(t);
  long long botleft = botLeft(t);
  long long botright = botRight(t);
  long long ret =
      square - tp - bt - lt - rt + topleft + topright + botleft + botright;
  return ret;
}
int main() {
  cin >> n >> x >> y >> c;
  long long lo = -1, hi = 1e9 + 1;
  while (hi - lo > 1) {
    long long mid = (lo + hi) / 2;
    if (getArea(mid) >= c) {
      hi = mid;
    } else {
      lo = mid;
    }
  }
  cout << lo + 1 << '\n';
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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>
#pragma GCC optimize("O3")
using namespace std;
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
template <typename T, size_t N>
int SIZE(const T (&t)[N]) {
  return N;
}
template <typename T>
int SIZE(const T &t) {
  return t.size();
}
string to_string(const string s, int x1 = 0, int x2 = 1e9) {
  return '"' + ((x1 < s.size()) ? s.substr(x1, x2 - x1 + 1) : "") + '"';
}
string to_string(const char *s) { return to_string((string)s); }
string to_string(const bool b) { return (b ? "true" : "false"); }
string to_string(const char c) { return string({c}); }
template <size_t N>
string to_string(const bitset<N> &b, int x1 = 0, int x2 = 1e9) {
  string t = "";
  for (int __iii__ = min(x1, SIZE(b)), __jjj__ = min(x2, SIZE(b) - 1);
       __iii__ <= __jjj__; ++__iii__) {
    t += b[__iii__] + '0';
  }
  return '"' + t + '"';
}
template <typename A, typename... C>
string to_string(const A(&v), int x1 = 0, int x2 = 1e9, C... coords);
int l_v_l_v_l = 0, t_a_b_s = 0;
template <typename A, typename B>
string to_string(const pair<A, B> &p) {
  l_v_l_v_l++;
  string res = "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
  l_v_l_v_l--;
  return res;
}
template <typename A, typename... C>
string to_string(const A(&v), int x1, int x2, C... coords) {
  int rnk = rank<A>::value;
  string tab(t_a_b_s, ' ');
  string res = "";
  bool first = true;
  if (l_v_l_v_l == 0) res += '\n';
  res += tab + "[";
  x1 = min(x1, SIZE(v)), x2 = min(x2, SIZE(v));
  auto l = begin(v);
  advance(l, x1);
  auto r = l;
  advance(r, (x2 - x1) + (x2 < SIZE(v)));
  for (auto e = l; e != r; e = next(e)) {
    if (!first) {
      res += ", ";
    }
    first = false;
    l_v_l_v_l++;
    if (e != l) {
      if (rnk > 1) {
        res += '\n';
        t_a_b_s = l_v_l_v_l;
      };
    } else {
      t_a_b_s = 0;
    }
    res += to_string(*e, coords...);
    l_v_l_v_l--;
  }
  res += "]";
  if (l_v_l_v_l == 0) res += '\n';
  return res;
}
void dbgm() { ; }
template <typename Heads, typename... Tails>
void dbgm(Heads H, Tails... T) {
  cout << to_string(H) << " | ";
  dbgm(T...);
}
const long long MOD = (int)1e9 + 7;
string ascii_lowercase = "abcdefghijklmnopqrstuvwxyz";
string ascii_uppercase = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
long long inv(long long a, long long b) {
  return 1 < a ? b - inv(b % a, a) * b / a : 1;
}
const long long INF = 1e6;
unordered_map<int, int, custom_hash> mp;
long long gcd(long long a, long long b, long long &x, long long &y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  long long x1, y1;
  long long d = gcd(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
long long distsq(long long x1, long long y1, long long x2, long long y2) {
  return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
}
long long n, x, y, c;
long long topArea(long long t) {
  long long topTip = x - t;
  long long len = max(0LL, 0 - topTip + 1);
  return len * len;
}
long long leftArea(long long t) {
  long long leftTip = y - t;
  long long len = max(0LL, 0 - leftTip + 1);
  return len * len;
}
long long rightArea(long long t) {
  long long rightTip = y + t;
  long long len = max(0LL, rightTip - n);
  return len * len;
}
long long botArea(long long t) {
  long long botTip = x + t;
  long long len = max(0LL, botTip - n);
  return len * len;
}
long long topLeft(long long t) {
  long long dist = x + y;
  long long len = max(0LL, t - dist + 1);
  return len * (len + 1) / 2;
}
long long topRight(long long t) {
  long long dist = (n + 1) - y + x;
  long long len = max(0LL, t - dist + 1);
  return len * (len + 1) / 2;
}
long long botRight(long long t) {
  long long dist = (n + 1) - y + (n + 1) - x;
  long long len = max(0LL, t - dist + 1);
  return len * (len + 1) / 2;
}
long long botLeft(long long t) {
  long long dist = (n + 1) - x + y;
  long long len = max(0LL, t - dist + 1);
  return len * (len + 1) / 2;
}
long long getArea(long long t) {
  long long square = 2 * t * (t + 1) + 1;
  long long tp = topArea(t);
  long long bt = botArea(t);
  long long lt = leftArea(t);
  long long rt = rightArea(t);
  long long topleft = topLeft(t);
  long long topright = topRight(t);
  long long botleft = botLeft(t);
  long long botright = botRight(t);
  long long ret =
      square - tp - bt - lt - rt + topleft + topright + botleft + botright;
  return ret;
}
int main() {
  cin >> n >> x >> y >> c;
  long long lo = -1, hi = 1e9 + 1;
  while (hi - lo > 1) {
    long long mid = (lo + hi) / 2;
    if (getArea(mid) >= c) {
      hi = mid;
    } else {
      lo = mid;
    }
  }
  cout << lo + 1 << '\n';
  return 0;
}

```