Problem Description

There are a total of $ N $ cards placed on a grid of $ H $ rows and $ W $ columns.

The $ i $ -th card has an integer $ A_i $ written on it and is placed on the square at the $ R_i $ -th row from the top and the $ C_i $ -th column from the left.

Multiple cards may be placed on the same square.

You can select up to one card from each row.

Then, you can select up to one card from each column.

Find the maximum sum of the integers written on the cards you have taken.

Input Format

The input is given from the standard input in the following format:

$ N $ $ H $ $ W $ $ R_1 $ $ C_1 $ $ A_1 $ $ R_2 $ $ C_2 $ $ A_2 $ $\vdots$ $ R_N $ $ C_N $ $ A_N $

Output Format

Output the maximum sum of the integers written on the cards you have taken.

Sample Input and Output

Sample Input #1

6 2 2
2 2 2
1 1 8
1 1 5
1 2 9
1 2 7
2 1 4

Sample Output #1

28

Sample Input #2

13 5 6
1 3 35902
4 6 19698
4 6 73389
3 6 3031
3 1 4771
1 4 4784
2 1 36357
2 1 24830
5 6 50219
4 6 22645
1 2 30739
1 4 68417
1 5 78537

Sample Output #2

430590

Sample Input #3

1 100000 100000
1 1 1

Sample Output #3

1

Notes/Hints

Constraints

• All inputs are integers.
• $1 \leq N \leq 10^5$
• $1 \leq H, W \leq 10^5$
• $1 \leq A_i \leq 10^5$
• $1 \leq R_i \leq H$
• $1 \leq C_i \leq W$

Sample Explanation 1

By taking the cards as follows, the sum of the integers written on the cards is $ 28 $, which is the maximum:
- Take the 4th card from the 1st row.
- Take the 6th card from the 2nd row.
- Take the 2nd card from the 1st column.
- Take the 5th card from the 2nd column.

见题面 Input 部分

见题面 Output 部分