One Clean Slice!

There is a tasty jelly. To make it easy to cut, the jelly is divided into unit cubes of volume 1: $R$ cells wide, $C$ cells deep and $H$ cells tall. The jelly holds $N$ raisins. No raisin spans more than one cell, and no cell holds two or more raisins. So the jelly can be read as a three dimensional array, and the position of a raisin is written as three integers $(r, c, h)$. See the figure below.

Tokkaengi wants to divide the jelly into exactly $N$ pieces so that every piece holds exactly one raisin. A cut follows cell boundaries exactly, goes all the way through the piece being cut and leaves two rectangular boxes; a cut cannot stop halfway. Among the $N$ pieces, Tokkaengi wants the smallest volume to be as large as possible. Help Tokkaengi cut the jelly.

The first line contains the jelly size $R$, $C$, $H$ and the number of raisins $N$, separated by spaces. ($1 \le R, C, H \le 7$, $1 \le N \le \min(R \times C \times H, 77)$)

Each of the next $N$ lines contains three integers $r$, $c$, $h$ giving the position of one raisin, separated by spaces. ($1 \le r \le R$, $1 \le c \le C$, $1 \le h \le H$) No two raisins share a position.

Print the largest volume the smallest piece can have when the jelly is divided into exactly $N$ pieces with one raisin in each piece.

This is the jelly of the example input seen from above. However well it is cut, the three pieces have volumes 2, 3 and 4.