## Description

Create a class in C++ to represent Students(similar to the previous assignment).

The class should have the following attributes:

● Marks of 5 subjects (No two students will have the same set of scores in all five subjects)

● Skill level(Two students can have the same skill level)

The condition for comparing arbitrary students A and B is:

● Rank(A) < Rank(B) if M1
(A)>M1

(B)

● Rank(A) < Rank(B) if Mi
(A)==Mi
(B) and Mi+1
(A)>Mi+1

(B) for i=1 to 4 where Mi

(A)

denotes marks of student A in subject i

Rank is defined as the position of a student in the sorted order using the above condition. It is

indexed from 1.

Let the skill levels of student A and student B (A ≠ B) be SA and SB

, and let their ranks be RA and

RB

. (A, B) is a special pair if A’s skill level is higher than B’s skill level, but A has a

greater(worse) rank than B, i.e. (A, B) is a special pair if SA > SB and RA > RB

Count the total number of special pairs.

(Hint: Merge-Sort)

Input Format

The first line contains the total number of students n.

Each of the following n lines contains 6 space-separated integers: marks of 5 subjects and skill

level.

n // Number of total students

n lines in the following format:

Output Format

A single integer denoting the number of special pairs.

Constraints

1 ≤ Number of students ≤ 10

5

1 ≤ Marks in any subject ≤ 10

3

1 ≤ Skill level ≤ 10

9

Subtasks

10 marks:

1 ≤ Number of students ≤ 5000

1 ≤ Marks in any subject ≤ 10

3

1 ≤ Skill level ≤ 10

9

5 marks:

1 ≤ Number of students ≤ 10

5

1 ≤ Marks in any subject ≤ 10

3

1 ≤ Skill level ≤ 10

2

10 marks:

1 ≤ Number of students ≤ 10

5

1 ≤ Marks in any subject ≤ 10

3

1 ≤ Skill level ≤ 10

9

Sample Testcase

Input:

5

1 2 3 4 5 5

2 3 4 5 1 4

3 4 5 1 2 3

4 5 1 2 3 2

5 1 2 3 4 1

Output:

10