#include <bits/stdc++.h>
using namespace std;
using pii = pair<long long, long long>;
const long long MOD = 1000000007;
const long long INF = 2000000000;
const long long DESPACITO = 1000000000000000000;
namespace minmax {
template <class T>
T max(T&& A) {
  return A;
}
template <class T>
T min(T&& A) {
  return A;
}
template <class T>
T max(T&& A, T&& B) {
  return A > B ? A : B;
}
template <class T>
T chmin2(T&& A, T&& B) {
  return A < B ? A : B;
}
template <class T, class... Ts>
T max(T&& A, Ts&&... ts) {
  T B = max(ts...);
  return A > B ? A : B;
}
template <class T, class... Ts>
T min(T&& A, Ts&&... ts) {
  T B = min(ts...);
  return A < B ? A : B;
}
template <class T, class... Ts>
T chmax(T&& A, Ts&&... ts) {
  A = max(A, ts...);
  return A;
}
template <class T, class... Ts>
T chmin(T&& A, Ts&&... ts) {
  A = min(A, ts...);
  return A;
}
template <class T1, class T2>
void chmin2(T1&& A, T2&& Aa, T1&& B, T2&& Bb) {
  if (B < A) A = B, Aa = Bb;
}
template <class T1, class T2>
void chmax2(T1&& A, T2&& Aa, T1&& B, T2&& Bb) {
  if (B > A) A = B, Aa = Bb;
}
}  // namespace minmax
namespace input {
template <class T>
void re(T&& Xx) {
  cin >> Xx;
}
template <class T1, class T2>
void re(pair<T1, T2>& Pp) {
  re(Pp.first);
  re(Pp.second);
}
template <class T>
void re(vector<T>& Aa) {
  for (long long i = 0; i < (long long)(Aa).size(); i++) re(Aa[i]);
}
template <class T1, class T2>
void rea(T1&& Aa, T2 t) {
  for (long long i = 0; i < t; i++) re(Aa[i]);
}
template <class T1, class T2, class... Ts>
void rea(T1&& Aa, T2 t, Ts&&... ts) {
  rea(Aa, t);
  rea(ts...);
}
template <class T1, class T2>
void rea1(T1&& Aa, T2 t) {
  for (long long i = 1; i <= t; i++) re(Aa[i]);
}
template <class T1, class T2, class... Ts>
void rea1(T1&& Aa, T2 t, Ts&... ts) {
  rea1(Aa, t);
  rea1(ts...);
}
template <class T, class... Ts>
void re(T&& t, Ts&... ts) {
  re(t);
  re(ts...);
}
}  // namespace input
namespace output {
void pr(int32_t Xx) { cout << Xx; }
void pr(bool Xx) { cout << Xx; }
void pr(long long Xx) { cout << Xx; }
void pr(long long unsigned Xx) { cout << Xx; }
void pr(double Xx) { cout << Xx; }
void pr(char Xx) { cout << Xx; }
void pr(const string& Xx) { cout << Xx; }
void pr(const char* Xx) { cout << Xx; }
void pr(const char* Xx, size_t len) { cout << string(Xx, len); }
void ps() { cout << "\n"; }
void pn() {}
void pw() { pr(" "); }
void pc() {
  pr("]");
  ps();
}
template <class T1, class T2>
void pr(const pair<T1, T2>& Xx) {
  pr(Xx.first);
  pw();
  pr(Xx.second);
}
template <class T>
void pr(const T&);
bool parse(const char* t) {
  if (t == "\n") return true;
  return false;
}
template <class T>
bool parse(T&& t) {
  return false;
}
template <class T1, class T2>
bool parsepair(const pair<T1, T2>& Xx) {
  return true;
}
template <class T>
bool parsepair(T&& t) {
  return false;
}
template <class T1, class T2>
void psa(T1&& Aa, T2 t) {
  for (long long i = 0; i < t; i++) pr(Aa[i]), pw();
  ps();
}
template <class T1, class T2>
void pna(T1&& Aa, T2 t) {
  for (long long i = 0; i < t; i++) pr(Aa[i]), ps();
}
template <class T1, class T2>
void psa2(T1&& Aa, T2 t1, T2 t2) {
  for (long long i = 0; i < t1; i++) {
    for (long long j = 0; j < t2; j++) pr(Aa[i][j]), pw();
    ps();
  }
}
template <class T>
void pr(const T& Xx) {
  if (!(long long)(Xx).size()) return;
  bool fst = 1;
  bool op = 0;
  if (parsepair(*Xx.begin())) op = 1;
  for (const auto& Aa : Xx) {
    if (!fst) pw();
    if (op) pr("{");
    pr(Aa), fst = 0;
    if (op) pr("}");
  }
}
template <class T, class... Ts>
void pr(const T& t, const Ts&... ts) {
  pr(t);
  pr(ts...);
}
template <class T, class... Ts>
void ps(const T& t, const Ts&... ts) {
  pr(t);
  if (sizeof...(ts)) {
    if (!parse(t)) pw();
  }
  ps(ts...);
}
template <class T>
void pn(const T& t) {
  for (const auto& Aa : t) ps(Aa);
}
template <class T, class... Ts>
void pw(const T& t, const Ts&... ts) {
  pr(t);
  if (sizeof...(ts)) pw();
  pw(ts...);
}
template <class T, class... Ts>
void pc(const T& t, const Ts&... ts) {
  bool op = 0;
  if (parsepair(t)) op = 1;
  if (op) pr("{");
  pr(t);
  if (op) pr("}");
  if (sizeof...(ts)) pr(", ");
  pc(ts...);
}
namespace trace {
template <class T1, class T2>
void __f(const char* name, const T1& Xx, const T2& y) {
  pr("[", y, "] = ");
  ps(Xx);
}
template <class T1, class T2, class... Ts>
void __f(const char* name, const T1& Xx, const T2& y, const Ts&... rest) {
  const char* open = strchr(name, '[');
  pr("[", y, "]");
  __f(open + 1, Xx, rest...);
}
template <class T1, class T2, class... Ts>
void __f0(const char* name, const T1& Xx, const T2& y, const Ts&... rest) {
  const char* open = strchr(name, '[');
  pr(name, size_t(open - name));
  __f(name, Xx, y, rest...);
}
template <class T>
void __fn(long long n, const char* name, const T& Xx) {
  for (long long i = 0; i < n; i++) pr(name), __f(name, Xx[i], i);
}
}  // namespace trace
}  // namespace output
using namespace minmax;
using namespace input;
using namespace output;
using namespace output::trace;
const long long N = 1e3 + 5;
long long a[N][N], R[N * N], C[N * N];
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long i, j, n, m, k, p, ans = -DESPACITO;
  re(n, m, k, p);
  multiset<long long, greater<long long>> rows, cols;
  for (i = 0; i < n; i++)
    for (j = 0; j < m; j++) re(a[i][j]);
  for (i = 0; i < n; i++) {
    long long sum = 0;
    for (j = 0; j < m; j++) sum += a[i][j];
    rows.insert(sum);
  }
  for (i = 0; i < m; i++) {
    long long sum = 0;
    for (j = 0; j < n; j++) sum += a[j][i];
    cols.insert(sum);
  }
  for (i = 1; i <= k; i++) {
    auto r = *rows.begin();
    R[i] = R[i - 1] + r;
    r -= m * p;
    rows.erase(rows.begin());
    rows.insert(r);
    auto c = *cols.begin();
    C[i] = C[i - 1] + c;
    c -= n * p;
    cols.erase(cols.begin());
    cols.insert(c);
  }
  for (i = 0; i <= k; i++) chmax(ans, R[i] + C[k - i] - i * (k - i) * p);
  ps(ans);
  return 0;
}

### Prompt

Your task is to create a Cpp solution to the following problem:

As we know, DZY loves playing games. One day DZY decided to play with a n × m matrix. To be more precise, he decided to modify the matrix with exactly k operations.

Each modification is one of the following:

  1. Pick some row of the matrix and decrease each element of the row by p. This operation brings to DZY the value of pleasure equal to the sum of elements of the row before the decreasing. 
  2. Pick some column of the matrix and decrease each element of the column by p. This operation brings to DZY the value of pleasure equal to the sum of elements of the column before the decreasing. 



DZY wants to know: what is the largest total value of pleasure he could get after performing exactly k modifications? Please, help him to calculate this value.

Input

The first line contains four space-separated integers n, m, k and p (1 ≤ n, m ≤ 103; 1 ≤ k ≤ 106; 1 ≤ p ≤ 100).

Then n lines follow. Each of them contains m integers representing aij (1 ≤ aij ≤ 103) — the elements of the current row of the matrix.

Output

Output a single integer — the maximum possible total pleasure value DZY could get.

Examples

Input

2 2 2 2
1 3
2 4


Output

11


Input

2 2 5 2
1 3
2 4


Output

11

Note

For the first sample test, we can modify: column 2, row 2. After that the matrix becomes:
    
    
      
    1 1  
    0 0  
      
    

For the second sample test, we can modify: column 2, row 2, row 1, column 1, column 2. After that the matrix becomes:
    
    
      
    -3 -3  
    -2 -2  
      
    

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using pii = pair<long long, long long>;
const long long MOD = 1000000007;
const long long INF = 2000000000;
const long long DESPACITO = 1000000000000000000;
namespace minmax {
template <class T>
T max(T&& A) {
  return A;
}
template <class T>
T min(T&& A) {
  return A;
}
template <class T>
T max(T&& A, T&& B) {
  return A > B ? A : B;
}
template <class T>
T chmin2(T&& A, T&& B) {
  return A < B ? A : B;
}
template <class T, class... Ts>
T max(T&& A, Ts&&... ts) {
  T B = max(ts...);
  return A > B ? A : B;
}
template <class T, class... Ts>
T min(T&& A, Ts&&... ts) {
  T B = min(ts...);
  return A < B ? A : B;
}
template <class T, class... Ts>
T chmax(T&& A, Ts&&... ts) {
  A = max(A, ts...);
  return A;
}
template <class T, class... Ts>
T chmin(T&& A, Ts&&... ts) {
  A = min(A, ts...);
  return A;
}
template <class T1, class T2>
void chmin2(T1&& A, T2&& Aa, T1&& B, T2&& Bb) {
  if (B < A) A = B, Aa = Bb;
}
template <class T1, class T2>
void chmax2(T1&& A, T2&& Aa, T1&& B, T2&& Bb) {
  if (B > A) A = B, Aa = Bb;
}
}  // namespace minmax
namespace input {
template <class T>
void re(T&& Xx) {
  cin >> Xx;
}
template <class T1, class T2>
void re(pair<T1, T2>& Pp) {
  re(Pp.first);
  re(Pp.second);
}
template <class T>
void re(vector<T>& Aa) {
  for (long long i = 0; i < (long long)(Aa).size(); i++) re(Aa[i]);
}
template <class T1, class T2>
void rea(T1&& Aa, T2 t) {
  for (long long i = 0; i < t; i++) re(Aa[i]);
}
template <class T1, class T2, class... Ts>
void rea(T1&& Aa, T2 t, Ts&&... ts) {
  rea(Aa, t);
  rea(ts...);
}
template <class T1, class T2>
void rea1(T1&& Aa, T2 t) {
  for (long long i = 1; i <= t; i++) re(Aa[i]);
}
template <class T1, class T2, class... Ts>
void rea1(T1&& Aa, T2 t, Ts&... ts) {
  rea1(Aa, t);
  rea1(ts...);
}
template <class T, class... Ts>
void re(T&& t, Ts&... ts) {
  re(t);
  re(ts...);
}
}  // namespace input
namespace output {
void pr(int32_t Xx) { cout << Xx; }
void pr(bool Xx) { cout << Xx; }
void pr(long long Xx) { cout << Xx; }
void pr(long long unsigned Xx) { cout << Xx; }
void pr(double Xx) { cout << Xx; }
void pr(char Xx) { cout << Xx; }
void pr(const string& Xx) { cout << Xx; }
void pr(const char* Xx) { cout << Xx; }
void pr(const char* Xx, size_t len) { cout << string(Xx, len); }
void ps() { cout << "\n"; }
void pn() {}
void pw() { pr(" "); }
void pc() {
  pr("]");
  ps();
}
template <class T1, class T2>
void pr(const pair<T1, T2>& Xx) {
  pr(Xx.first);
  pw();
  pr(Xx.second);
}
template <class T>
void pr(const T&);
bool parse(const char* t) {
  if (t == "\n") return true;
  return false;
}
template <class T>
bool parse(T&& t) {
  return false;
}
template <class T1, class T2>
bool parsepair(const pair<T1, T2>& Xx) {
  return true;
}
template <class T>
bool parsepair(T&& t) {
  return false;
}
template <class T1, class T2>
void psa(T1&& Aa, T2 t) {
  for (long long i = 0; i < t; i++) pr(Aa[i]), pw();
  ps();
}
template <class T1, class T2>
void pna(T1&& Aa, T2 t) {
  for (long long i = 0; i < t; i++) pr(Aa[i]), ps();
}
template <class T1, class T2>
void psa2(T1&& Aa, T2 t1, T2 t2) {
  for (long long i = 0; i < t1; i++) {
    for (long long j = 0; j < t2; j++) pr(Aa[i][j]), pw();
    ps();
  }
}
template <class T>
void pr(const T& Xx) {
  if (!(long long)(Xx).size()) return;
  bool fst = 1;
  bool op = 0;
  if (parsepair(*Xx.begin())) op = 1;
  for (const auto& Aa : Xx) {
    if (!fst) pw();
    if (op) pr("{");
    pr(Aa), fst = 0;
    if (op) pr("}");
  }
}
template <class T, class... Ts>
void pr(const T& t, const Ts&... ts) {
  pr(t);
  pr(ts...);
}
template <class T, class... Ts>
void ps(const T& t, const Ts&... ts) {
  pr(t);
  if (sizeof...(ts)) {
    if (!parse(t)) pw();
  }
  ps(ts...);
}
template <class T>
void pn(const T& t) {
  for (const auto& Aa : t) ps(Aa);
}
template <class T, class... Ts>
void pw(const T& t, const Ts&... ts) {
  pr(t);
  if (sizeof...(ts)) pw();
  pw(ts...);
}
template <class T, class... Ts>
void pc(const T& t, const Ts&... ts) {
  bool op = 0;
  if (parsepair(t)) op = 1;
  if (op) pr("{");
  pr(t);
  if (op) pr("}");
  if (sizeof...(ts)) pr(", ");
  pc(ts...);
}
namespace trace {
template <class T1, class T2>
void __f(const char* name, const T1& Xx, const T2& y) {
  pr("[", y, "] = ");
  ps(Xx);
}
template <class T1, class T2, class... Ts>
void __f(const char* name, const T1& Xx, const T2& y, const Ts&... rest) {
  const char* open = strchr(name, '[');
  pr("[", y, "]");
  __f(open + 1, Xx, rest...);
}
template <class T1, class T2, class... Ts>
void __f0(const char* name, const T1& Xx, const T2& y, const Ts&... rest) {
  const char* open = strchr(name, '[');
  pr(name, size_t(open - name));
  __f(name, Xx, y, rest...);
}
template <class T>
void __fn(long long n, const char* name, const T& Xx) {
  for (long long i = 0; i < n; i++) pr(name), __f(name, Xx[i], i);
}
}  // namespace trace
}  // namespace output
using namespace minmax;
using namespace input;
using namespace output;
using namespace output::trace;
const long long N = 1e3 + 5;
long long a[N][N], R[N * N], C[N * N];
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long i, j, n, m, k, p, ans = -DESPACITO;
  re(n, m, k, p);
  multiset<long long, greater<long long>> rows, cols;
  for (i = 0; i < n; i++)
    for (j = 0; j < m; j++) re(a[i][j]);
  for (i = 0; i < n; i++) {
    long long sum = 0;
    for (j = 0; j < m; j++) sum += a[i][j];
    rows.insert(sum);
  }
  for (i = 0; i < m; i++) {
    long long sum = 0;
    for (j = 0; j < n; j++) sum += a[j][i];
    cols.insert(sum);
  }
  for (i = 1; i <= k; i++) {
    auto r = *rows.begin();
    R[i] = R[i - 1] + r;
    r -= m * p;
    rows.erase(rows.begin());
    rows.insert(r);
    auto c = *cols.begin();
    C[i] = C[i - 1] + c;
    c -= n * p;
    cols.erase(cols.begin());
    cols.insert(c);
  }
  for (i = 0; i <= k; i++) chmax(ans, R[i] + C[k - i] - i * (k - i) * p);
  ps(ans);
  return 0;
}

```