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G - Dream Team

Score : $600$ points

Problem Statement

There are $N$ competitive programmers.
The $i$-th competitive programmer belongs to University $A_i$, is good at Subject $B_i$, and has a power of $C_i$.

Consider a team consisting of some of the $N$ people. Let us call such a team a dream team if both of the following conditions are satisfied:

• Any two people belonging to the team belong to different universities.
• Any two people belonging to the team are good at different subjects.

Let $k$ be the maximum possible number of members of a dream team. For each $i=1,2,\ldots,k$, solve the following question.

Question: find the maximum sum of power of people belonging to a dream team consisting of $i$ people.

Constraints

• $1 \leq N \leq 3\times 10^4$
• $1 \leq A_i,B_i \leq 150$
• $1 \leq C_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $B_1$ $C_1$

$A_2$ $B_2$ $C_2$

$\vdots$

$A_N$ $B_N$ $C_N$

Output

Let $k$ be the maximum possible number of members of a dream team.
Print $k$ in the first line. Then, print $k$ more lines, each containing the answer to the question for $i=1,2,\ldots,k$, in this order.

3
1 1 100
1 20 10
2 1 1

2
100
11

• The sum of power of members of a dream team consisting of exactly $1$ person is $100$, when the team consists of the $1$-st competitive programmer.
• The sum of power of members of a dream team consisting of exactly $2$ people is $11$, when the team consists of the $2$-nd and the $3$-rd competitive programmers.
• It is impossible to form a dream team consisting of exactly $3$ people.

10
1 4 142135623
2 6 457513110
3 1 622776601
5 1 961524227
2 2 360679774
2 4 494897427
3 7 416573867
5 2 915026221
1 7 320508075
5 3 851648071

4
961524227
1537802822
2032700249
2353208324