AT_arc215_c [ARC215C] Strong Surname

There are $ N $ people with distinct surnames, and the surname of the $ i $ -th person has parameters $ (X_i, Y_i, Z_i) $ . Different surnames may have identical parameters. The following event occurs $ N - 1 $ times. - Two people become parents and one child appears. The two parents die. The child chooses the stronger of the two parents' surnames as their own. A surname with parameters $ (x_1, y_1, z_1) $ is stronger than a surname with parameters $ (x_2, y_2, z_2) $ if $ x_1 > x_2 $ , $ y_1 > y_2 $ , and $ z_1 > z_2 $ all hold. If neither parent's surname is stronger than the other's, the child randomly chooses one of the two parents' surnames. Find the number of people among the $ N $ people whose surname can be the surname of the last remaining person. You are given $ T $ test cases; solve each one.

The input is given from Standard Input in the following format: > $ T $ $ \text{case}_1 $ $ \text{case}_2 $ $ \vdots $ $ \text{case}_T $ Each test case is given in the following format: > $ N $ $ X_1 $ $ Y_1 $ $ Z_1 $ $ X_2 $ $ Y_2 $ $ Z_2 $ $ \vdots $ $ X_N $ $ Y_N $ $ Z_N $

Output $ T $ lines. The $ i $ -th line should contain the number of people whose surname can be the surname of the last remaining person for the $ i $ -th test case.

### Sample Explanation 1 For the first test case, below is a possible sequence of events. Let surname $ i $ denote the surname of the $ i $ -th person. - The people with surnames $ 2 $ and $ 4 $ become parents. Surname $ 2 $ is stronger, so the child has surname $ 2 $ . - The people with surnames $ 2 $ and $ 3 $ become parents. Surname $ 3 $ is stronger, so the child has surname $ 3 $ . - The people with surnames $ 1 $ and $ 3 $ become parents. Neither surname $ 1 $ nor surname $ 3 $ is stronger than the other, so the child chooses either surname $ 1 $ or $ 3 $ . Neither surname $ 2 $ nor surname $ 4 $ can be the surname of the last remaining person, so the answer is $ 2 $ . ### Constraints - $ 1 \le T \le 2 \times 10^5 $ - $ 2 \le N \le 2 \times 10^5 $ - $ 1 \le X_i, Y_i, Z_i \le N $ - The sum of $ N $ over all test cases is at most $ 2 \times 10^5 $ . - All input values are integers.