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.

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.

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.

Sample Input 1

3
1 1 100
1 20 10
2 1 1

Sample Output 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.

Sample Input 2

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

Sample Output 2

4
961524227
1537802822
2032700249
2353208324

见题面 Input 部分

见题面 Output 部分