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B. DZY Loves Modification

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAs 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:

- 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. - 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* ≤ 10^{3}; 1 ≤ *k* ≤ 10^{6}; 1 ≤ *p* ≤ 100).

Then *n* lines follow. Each of them contains *m* integers representing *a*_{ij} (1 ≤ *a*_{ij} ≤ 10^{3}) — 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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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