Sheep in the hall#4355
Sheep Alina tries to look smart; for that, she even wears glasses (although in photos she is without them). But the problem is that she is very talkative. Perhaps it helps her in the programming contest, but all who are in close proximity to her are not happy. For her, nothing is sacred; she can talk anywhere, whether it is a lecture or a parsing. Let there be rows in the hall; each row has seats. Alina chooses seat in row number . Owners of seats whose Manhattan distance to Alina does not exceed can, in general, not take the pen and notes, because they will not hear anyone but Alina. Everyone is already tired of it, and everyone wants to stay as far away from Alina as possible to safely enjoy the informative lecturer’s speech. What is the minimum number of listeners who will inevitably be within Alina’s sound range, if everyone sits as far away from her as possible? (One seat can contain no more than one listener.)
Recall that the Manhattan distance between points (x_1, y_1) and (x_2, y_2) is defined to be equal to |x_1 - x_2| + |y_1 - y_2|.
The only line of input contains six integers: the number of rows in the hall (1 \leq N \leq 10^9), the number of seats in each row (1 \leq M \leq 10^9), the number of listeners (not including Alina) (P < N \times M), (1 \leq x \leq N), (1 \leq y \leq M) — the coordinates of Alina’s location, and the number .
Output the minimum possible number of listeners who will be within Alina's sound range.
Example 1