Description

Student $\mathrm{A}$ dreams that he is standing on a platform. Around him there are some plane mirrors, and we assume his position is $(0,0)$.

He finds that each plane mirror has an initial opacity, denoted by $v_i$.

In what follows, we define:

• The “opacity” of a ray as: the sum of the initial opacities of all plane mirrors that the ray passes through.

• The “visual opacity” of a plane mirror as: the maximum opacity among all rays that originate from $(0,0)$ and pass through that plane mirror.

Student $\mathrm{A}$ suddenly discovers that he can control these plane mirrors, so the following problem arises.

Student $\mathrm{A}$ needs you to perform the following operations:

1 x1 y1 x2 y2 v: Create a plane mirror whose two endpoints are at $(x_1,y_1),(x_2,y_2)$, with initial opacity $v$.

2 d: Destroy the $d$-th created plane mirror. It is guaranteed that it has not been destroyed.

3 x y: Let $\mathrm{A=(0,0),B=(x,y)}$. Query the opacity of the ray $\mathrm{AB}$.

4 d: Query the visual opacity of the $d$-th plane mirror. If it has been destroyed, output oops!.

Input Format

The first line contains an integer $n$, denoting the number of operations.

The next $n$ lines: the $i$-th line starts with an integer $opt$, and then:

• If $opt=1$, five integers $x_1,y_1,x_2,y_2,v$.

• If $opt=3$, two integers $x,y$.

• Otherwise, one integer $d$.

Output Format

For each query of type $3$ or $4$, output one line with the answer.

11
1 -1 2 2 -1 7
1 2 2 -1 0 10
1 2 1 1 -1 17
3 5 4
3 -99999 0
3 -3 6
3 1 -1
4 2
2 1
4 2
4 1

7
10
17
17
17
10
oops!

Hint

Sample Explanation

As shown in the figure, blue represents rays and red represents plane mirrors.

For the 1st query: we can see the ray only passes through plane mirror $1$, so the answer is $7$.

For the 2nd query: we can see the ray only passes through plane mirror $2$, so the answer is $10$.

For the 3rd query: we can see the ray passes through plane mirrors $1,2$, so the answer is $7+10=17$.

For the 4th query: we can see the ray passes through plane mirror $3$, so the answer is $17$.

For the 5th query: we can see that among rays passing through plane mirror $2$, the ray with the maximum opacity is $(0,0)(2,2)$ (the ray is not unique). It passes through plane mirrors $1,2$, so the answer is $7+10=17$.

For the 6th query: we can see that among rays passing through plane mirror $2$, the ray with the maximum opacity is $(0,0)(2,2)$ (the ray is not unique). It passes through plane mirror $2$, so the answer is $10$.

For the 7th query: since plane mirror $1$ has been destroyed, output oops!.

Constraints and Notes

For $100\%$ of the testdata, $1\leq n\leq 2\times 10^5$, $1\leq v\leq 10^3$, and $0\leq |x|,|y|\leq 10^5$.

It is guaranteed that the total number of plane mirrors will not exceed $10^5$.

It is guaranteed that no plane mirror passes through $(0,0)$, but it is not guaranteed that a plane mirror will not degenerate into a point.

It is guaranteed that for all type $3$ queries, $(x,y)\neq(0,0)$.

For all test points, the time limit is $2\mathrm{s}$ and the memory limit is $128\mathrm{MB}$.

Translated by ChatGPT 5