Combine Two Elements

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 | \ leq Take out and delete the element $ 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

inputFormat

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.

outputFormat

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

样例

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

5