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Problems

Sheep in the hall

Sheep in the hall

Time limit 1 second
Memory limit 64 MiB

Sheep Alina tries to look smart, for that she even wears glasses (although on photos she’s without them). But the problem is that she’s very talkative. Perhaps it helps her in the programming contest, but all who are in close proximity to her, aren’t happy. For her, nothing is sacred, she can talk anywhere, whether it's a lecture, or parsing. Let in the hall are N rows, each row has M seats. Alina choses a seat y in the row number x. Owners of seats whose Manhattan distance to Alina doesn’t exceed R, can, in general, don’t take the pen and notes, because they will not hear anyone but the damn sheep. Everyone is already tired of it, and everyone wants to stay as far away from Aline to safely enjoy the informative lecturer’s speech. What is the minimum number of victims that will inevitably fall into Alina’s sound-web, if all sit as far away from her? (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|.

Input data

The only line of input contains six integers: the number of rows in the hall N (1 N10^9), the number of seats in each row M (1 M10^9), the number of listeners (not including Alina) P (P < N*M), x (1 xN) and y (1 yM) - coordinates of Alina’s location, and the number R.

Output data

The minimum possible number of Alina’s victims.

Examples

Input example #1
3 3 8 2 2 1
Output example #1
4
Author Борис Соколов
Source Дистанционная Летняя Компьютерная Школа - лето 2013 года