Problem H. Health and light

Author:Антон Карабанов   Time limit:1 sec
Input file:Standard input   Memory limit:512 Mb
Output file:Standard output  

Statement

The city of N has a happy event! On the single street of the city, new street lamp will be installed and the new pharmacy will open. Help the city governor to find optimal places for these objects.

The street is represented by a segment of coordinate axis, where the leftmost house has coordinate 0. Let's assume house sizes to be negligibly small compared to the street length and represent houses as points on the axis.

The lamp has "brightness" parameter expressing the largest distance from the lamp where the light reaches. For example when brightness is equal to 10, lamp installed at the point x = 25 will light the street on the segment from 15 to 35 inclusive.

The pharmacy has "remoteness" parameter expressing the largest distance from it to the house such that people from that house will still visit. For example when remoteness is equal to 100, pharmacy located at point x = 25, will be visited by people living in houses with coordinates from 0 to 125 inclusive (there are no houses with negative coordinates).

Input format

First line of input contains three integers separated by spaces: n — number of houses, a — brightness и b — remoteness. Next n lines contain two space-separated integers each: xi, qi — coordinate of the house and number of people living in it (houses may be empty).

Output format

Output two integers — maximum number of houses illuminated by the lamp and maximum number of people who will visit the pharmacy. Both lamp and pharmacy may be located between the houses as well as at points with the coordinate of some house.

Constraints

1 ≤ n, a, b ≤ 105

0 ≤ xi, qi ≤ 109

Notes on sample

Sample contains five houses, lamp brightness 15 and pharmacy remoteness 20. Lamp can be installed at either point 15, or point 25, in both cases 4 houses will be illuminated. Pharmacy may be located at point 20, in which case all city inhabitants will be able to visit.

Sample tests

No. Standard input Standard output
1
5 15 20
0 6
10 5
20 0
30 7
40 10
4 28

0.126s 0.013s 13