3676 -- Tomorrow Genius 2008

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Tomorrow Genius 2008

Time Limit: 5000MS		Memory Limit: 65536K
Total Submissions: 105		Accepted: 18

Description

Tomorrow Genius Contest is a traditional event of Daisy Hill Primary School for the purpose of promoting the spirit of its motto, "Mens et Manus" among the students. This year's rules are quite simple: Given N triangles, the contestants are asked to piece them together to make a rectangle with width W and height H as rapidly and possible. The contestants are allowed to move, rotate but not turn over the triangles. The first one who achieves the goal is the winner of the contest.

Of course the host doesn't want to hold a no-winner contest. So he asks you, the technology support of the contest, to determine whether a problem is solvable.

Input

The first line contains three integers, N (1 ≤ N ≤ 10), W (1 ≤ W ≤ 10), H (1 ≤ H ≤ 10).
The following N lines contain six integers x₁, y₁, x₂, y₂, x₃, y₃ (-100 ≤ x_i, y_i ≤ 100) each, describing the coordinates of the vertices of a triangle each.

Output

One line contains "YES" or "NO" indicating whether the problem is solvable.

Sample Input

Sample Input 16 5 5
0 0 0 3 4 0
0 0 0 3 4 0
0 0 0 3 4 0
0 0 0 3 4 0
0 0 0 1 1 0
0 0 0 1 1 0 Sample Input 25 5 5
0 0 0 3 4 0
0 0 0 3 4 0
0 0 0 3 4 0
0 0 0 3 4 0
0 0 0 1 2 0

Sample Output

Sample Output 1YES Sample Output 2NO

Source

POJ Founder Monthly Contest – 2008.07.27, Dagger