Choose a Square

Description:

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.

Sample Input:

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

Sample Output:

4
1 1 3 3

Sample Input:

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

Sample Output:

0
1 1 1 1

Note:

The field corresponding to the first example: