Problem

Given $ N $ a pair of non-negative integers $ (a_i, b_i) $ and non-negative integers $ A $, $ B $.
I want to do as many of the following operations as possible.

• $| a_i --b_i | \ leq A$ or $B \ leq | a_i --b_i | \$ i $ that satisfies 2A $
• $| (a_i + a_j)-(b_i + b_j) | \ leq A$ or $B \ leq | (a_i + a_j)-(b_i + b_j) | Extract and delete the pair of j$ ($i \ neq j$)

Find the maximum number of operations.

Constraints

The input satisfies the following conditions.

• $1 \ leq N \ leq 800$
• $0 \ leq A, B \ leq 10 ^ 5$
• $0 \ leq a_i, b_i \ leq 10 ^ 5$
• $A \ leq B$ and $B \ leq 2A$

Input

The input is given in the following format.

$ N $ $ A $ $ B $
$ a_1 $ $ b_1 $
$ a_2 $ $ b_2 $
...
$ a_N $ $ b_N $

All inputs are given as integers.
$ N $, $ A $, $ B $ are given on the first line, separated by blanks.
The $ i $ th pair $ a_i $ and $ b_i $ ($1 \ leq i \ leq N$) are given in the second and subsequent $ N $ lines, separated by blanks.

Output

Output the maximum number of operations on one line.

Examples

Input

5 3 5
7 2
13 1
1 1
2 9
2 4

Output

4

Input

10 7 12
34 70
36 0
12 50
76 46
33 45
61 21
0 1
24 3
98 41
23 84

Output

5

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