Description

Little W enjoys adapting problems.

There are two types of adaptations: problem statement adaptation and solution approach adaptation.

There are $n$ candidate problems, each with an initial quality $a_i$ and two attributes $x_i$ and $y_i$. If $x_i=1$, it means the problem is a problem statement adaptation; if $y_i=1$, it means the problem is a solution approach adaptation.

When reviewing a problem:

• If it is a problem statement adaptation, its perceived quality decreases by $k_1$
• If it is a solution approach adaptation, its perceived quality decreases by $k_2$
• If it is both adaptations, it is discarded
• If the perceived quality becomes negative, it is discarded

Find the maximum perceived quality among remaining problems. If all are discarded, output -1.

Input Format

First line: three integers $n$, $k_1$, $k_2$

Next $n$ lines: three integers each ($a_i$, $x_i$, $y_i$)

Output Format

Single integer: the maximum perceived quality, or -1 if all discarded

4 1 2
6 0 0
7 0 0
6 1 1
9 1 0 

8

Hint

Sample Breakdown:

1. Problem 1: $6$ (no adaptations)
2. Problem 2: $7$ (no adaptations)
3. Problem 3: discarded (both adaptations)
4. Problem 4: $9-1=8$ (statement adaptation)

Maximum quality among remaining: $8$

Data Range

For all data $1 \le n \le 10^5$, $1 \le a_i, k_1, k_2 \le 10^9$,$x_i, y_i \in \{0,1\}$,No bundled testing.