Problem Description

Given a positive integer $m$, you need to maintain an $m \times m$ matrix $a_{i,j},\;1\le i,j\le m$, with initial values all $0$.

There are $m$ operations. Each operation gives $x,\;y,\;z_{0,0},\;z_{0,1},\;z_{1,0},\;z_{1,1}$.

First, for each $0\le p,q\le 1$, query the maximum value of $a_{i,j}$ among all positions in the matrix that satisfy $[i\ge x]=p,\;[j\ge y]=q$. Denote the answer as $w_{p,q}$.

Then, for every position $(i,j)$ in the matrix, add $z_{[i\ge x],[j\ge y]}$ to $a_{i,j}$.

The notation $[c]$ equals $1$ when the condition $c$ is true, and $0$ otherwise.

Input Format

The first line contains one positive integer $m$.

Then follow $m$ lines. Each line contains $6$ numbers $x,\;y,\;z_{0,0},\;z_{0,1},\;z_{1,0},\;z_{1,1}$ representing one operation, with the meaning described above.

Output Format

For each operation, output $4$ lines, in order: $w_{0,0},\;w_{0,1},\;w_{1,0},\;w_{1,1}$.

10
2 8 9 5 4 2
7 10 3 7 2 10
10 5 4 2 8 3
8 8 7 6 8 4
3 2 5 3 2 9
3 3 9 10 5 6
4 8 2 9 3 2
4 5 5 10 1 1
9 4 10 2 1 4
6 9 7 2 4 6

0
0
0
0
9
5
4
2
12
12
6
12
16
14
14
15
23
23
22
22
28
26
31
31
37
33
37
35
39
42
40
37
44
52
41
41
54
54
47
41

Hint

Idea: ?, Solution: ?, Code: ccz181078, Data: ccz181078.

For $100\%$ of the testdata, $2 \le x,y\le m\le 2\times 10^5$, $1\le z_{i,j}\le 10^9$, and all values are integers.

Translated by ChatGPT 5