402908: GYM100942 I Manhattan Project

In a seven-dimensional space there is a six-dimensional institution where five-dimensional workers run a four-dimensional data base. The database contains information about the points defined by four coordinated. The institution receives three kinds of requests :

1. Add a point with the given coordinates
2. Delete a point with the given coordinates.
3. Provide a distance between the given point and the most distant point.

In this space the distance between the points (x₁, x₂, x₃, x₄) and (y₁, y₂, y₃, y₄) is calculated as |x₁ - y₁| + |x₂ - y₂| + |x₃ - y₃| + |x₄ - y₄|.

There going to be some staff reduction in the institution, so it is necessary to have the above mentioned work automated.

The first line contains an integer N (1 ≤ N ≤ 10⁵) — a number of requests. Each of the next N lines contains five integers: t, x₁, x₂, x₃, x₄ — a kind of request and four coordinates of the point respectively (1 ≤ t ≤ 3,  - 10⁸ ≤ x₁, x₂, x₃, x₄ ≤ 10⁸).

It is guaranteed that at the moment of request of type 1 (add) the point (x₁, x₂, x₃, x₄) does not exist, at the moment of request of type 2 (delete) the point (x₁, x₂, x₃, x₄) exists, at the moment of request of type 3 (distance request) at least one point exists. There is no points in the database until the first request arrives.

For each request of 3 kind output the request's result in a separate line.

5
1 0 0 0 0
1 -10 2 6 -9
3 -8 0 9 -5
2 0 0 0 0
3 -8 0 9 -5

22
11

9
1 2 0 0 0
1 4 3 0 0
1 1 5 0 0
3 2 3 0 0
3 -1 2 0 0
2 4 3 0 0
3 -1 2 0 0
2 2 0 0 0
3 1 5 0 0

3
6
5
0