A new robot "PTZ07" is now in the testing room. The testing room
is a parallelepiped n × m × k. The robot knows a sequence
of instructions to execute. The instructions are:
'u' — one position up, 'd' — one position down,
'l' — one position left, 'r' — one position right,
'f' — one position forward, 'b' — one position backward.
Robot executes its program one by one. If the instruction
tells the robot to go outside the room, the robot ignores this instruction.
You are given a sequence of instructions, but you don't know the initial
location of the robot. Your task is to find the number of
positions in which the robot may finish its trip.
The first line of the input contains three integers
n, m and k (1 ≤ n, m, k ≤ 105) —
width (left-right dimension), height (up-down dimension) and length
(forward-backward dimension). The second line
contains the sequence of instructions. There will be no more than 105
Output the number of positions where robot may finish its trip after
executing the given program.
1 1 1
2 2 2
13 14 15
Problem Author: Dmitry Gozman
Problem Source: Dmitry Gozman Contest 1, Petrozavodsk training camp, January 2007