Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

binary search

data structures

sortings

*2400

No tag edit access

The problem statement has recently been changed. View the changes.

×
F. Choose a Square

time limit per test

6 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPetya recently found a game "Choose a Square". In this game, there are $$$n$$$ points numbered from $$$1$$$ to $$$n$$$ on an infinite field. The $$$i$$$-th point has coordinates $$$(x_i, y_i)$$$ and cost $$$c_i$$$.

You have to choose a square such that its sides are parallel to coordinate axes, the lower left and upper right corners belong to the line $$$y = x$$$, and all corners have integer coordinates.

The score you get is the sum of costs of the points covered by the selected square minus the length of the side of the square. Note that the length of the side can be zero.

Petya asks you to calculate the maximum possible score in the game that can be achieved by placing exactly one square.

Input

The first line of the input contains one integer $$$n$$$ ($$$1 \le n \le 5 \cdot 10^5$$$) — the number of points on the field.

Each of the following $$$n$$$ lines contains three integers $$$x_i, y_i, c_i$$$ ($$$0 \le x_i, y_i \le 10^9, -10^6 \le c_i \le 10^6$$$) — coordinates of the $$$i$$$-th point and its cost, respectively.

Output

In the first line print the maximum score Petya can achieve.

In the second line print four integers $$$x_1, y_1, x_2, y_2$$$ ($$$0 \le x_1, y_1, x_2, y_2 \le 2 \cdot 10^9, x_1 = y_1, x_2 = y_2, x_1 \le x_2$$$) separated by spaces — the coordinates of the lower left and upper right corners of the square which Petya has to select in order to achieve the maximum score.

Examples

Input

6 0 0 2 1 0 -5 1 1 3 2 3 4 1 4 -4 3 1 -1

Output

4 1 1 3 3

Input

5 3 3 0 3 3 -3 0 2 -1 3 1 3 0 0 -2

Output

0 1 1 1 1

Note

The field corresponding to the first example:

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/13/2024 22:49:15 (k1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|