E. The Cells on the Papertime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputOn an endless checkered sheet of paper, n cells are chosen and colored in three colors, where n is divisible by 3. It turns out that there are exactly \frac{n}{3} marked cells of each of three colors! Find the largest such k that it's possible to choose \frac{k}{3} cells of each color, remove all other marked cells, and then select three rectangles with sides parallel to the grid lines so that the following conditions hold:  No two rectangles can intersect (but they can share a part of the boundary). In other words, the area of intersection of any two of these rectangles must be 0. The i-th rectangle contains all the chosen cells of the i-th color and no chosen cells of other colors, for i = 1, 2, 3. InputThe first line of the input contains a single integer n — the number of the marked cells (3 \leq n \le 10^5, n is divisible by 3).The i-th of the following n lines contains three integers x_i, y_i, c_i (|x_i|,|y_i| \leq 10^9; 1 \leq c_i \leq 3), where (x_i, y_i) are the coordinates of the i-th marked cell and c_i is its color.It's guaranteed that all cells (x_i, y_i) in the input are distinct, and that there are exactly \frac{n}{3} cells of each color.OutputOutput a single integer k — the largest number of cells you can leave.ExamplesInput
9
2 3 1
4 1 2
2 1 3
3 4 1
5 3 2
4 4 3
2 4 1
5 2 2
3 5 3
Output
6
Input
3
1 1 1
2 2 2
3 3 3
Output
3
NoteIn the first sample, it's possible to leave 6 cells with indexes 1, 5, 6, 7, 8, 9.In the second sample, it's possible to leave 3 cells with indexes 1, 2, 3.
9
2 3 1
4 1 2
2 1 3
3 4 1
5 3 2
4 4 3
2 4 1
5 2 2
3 5 3

6 
['binary search', 'implementation', 'sortings', '*2800']