Score : 200 points

Problem Statement

There are N rectangular plate materials made of special metal called AtCoder Alloy. The dimensions of the i-th material are A_i \times B_i (A_i vertically and B_i horizontally).

Takahashi wants a rectangular plate made of AtCoder Alloy whose dimensions are exactly H \times W. He is trying to obtain such a plate by choosing one of the N materials and cutting it if necessary. When cutting a material, the cuts must be parallel to one of the sides of the material. Also, the materials have fixed directions and cannot be rotated. For example, a 5 \times 3 material cannot be used as a 3 \times 5 plate.

Out of the N materials, how many can produce an H \times W plate if properly cut?

Constraints

  • 1 \leq N \leq 1000
  • 1 \leq H \leq 10^9
  • 1 \leq W \leq 10^9
  • 1 \leq A_i \leq 10^9
  • 1 \leq B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N H W
A_1 B_1
A_2 B_2
:
A_N B_N

Output

Print the answer.

Sample Input 1

3 5 2
10 3
5 2
2 5

Sample Output 1

2

Takahashi wants a 5 \times 2 plate.

  • The dimensions of the first material are 10 \times 3. We can obtain a 5 \times 2 plate by properly cutting it.
  • The dimensions of the second material are 5 \times 2. We can obtain a 5 \times 2 plate without cutting it.
  • The dimensions of the third material are 2 \times 5. We cannot obtain a 5 \times 2 plate, whatever cuts are made. Note that the material cannot be rotated and used as a 5 \times 2 plate.

Sample Input 2

10 587586158 185430194
894597290 708587790
680395892 306946994
590262034 785368612
922328576 106880540
847058850 326169610
936315062 193149191
702035777 223363392
11672949 146832978
779291680 334178158
615808191 701464268

Sample Output 2

8