Trouble! A meteorite is approaching the city of N. People have already managed to evacuate, but damage to houses cannot be avoided. Scientists have already figured out where the meteorite will fall. You, as an employee of an insurance company, have been asked to find out the number of houses that will be affected by a meteorite fall.
Let us introduce a rectangular coordinate system on the plane. The city is a rectangle n × m . Its lower left corner is located at the point with coordinates (0, 0) , and its upper right corner at the point with coordinates ( n - 1, m - 1) . At each point with integer coordinates inside or on the border of this rectangle, there is a house. The houses in city N are small, so they can be considered dots.
It is known that the meteorite fell to the point ( x , y ) , and the radius of its impact is equal to r . Thus, all the houses of the city at a distance of no more than r from the point of impact of the meteorite will be damaged. Find the number of houses that will be damaged.
Input
The first line contains two integers n , m ( 1 ≤ n , m ≤ 500 ) — dimensions of the city N.
The second line contains three integers x , y , r ( - 500 ≤ x , y ≤ 500 ; 0 ≤ r ≤ 500 ) — coordinates of the impact point of the meteorite and the radius of damage, respectively.
Imprint
Print one number — number of damaged houses.
Note
Illustration for the test from the example: black dots indicate damaged houses, white — survivors.
Examples
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Input |
Output |
| 1 |
2 3
1 2 1
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