You are taking your calculus exam. In the exam room, there is an ~N \times N~ grid of desks, each with exactly one student taking an exam at that desk.

Your teacher has come up with an interesting way of grading the exams. Let ~p_{i,j}~ represent the initial mark that the student at position ~(i,j)~ got on the exam. His actual mark, ~a_{i,j}~, is equal to ~a_{i,j} = p_{i,j} + k_{i,j}~ where ~k_{i,j}~ is the number of students who have an actual mark higher than or equal to student ~(i,j)~'s initial mark and their position is ~(x,y)~ where ~1 \le x < i~ and ~1 \le y < j~. Formally, ~k_{i,j}~ is the number of students where ~a_{x,y} \ge p_{i,j}~ and ~1 \le x < i, 1 \le y < j~.

Wanting to know how much everyone's marks change, you are to find the sum of ~k_{i,j}~ for all ~i, j~ ~(1 \le i,j \le N)~.

Input Specification

The first line will contain the ~N~ ~(1 \le N \le 800)~.

The next line will contain ~N~ lines will each contain ~N~ space-separated integers ~p_{i,j}~ ~(1 \le p_{i,j} \le 10^9)~.

Output Specification

Output the sum of all ~k_{i,j}~, as defined above.

Sample Input 1

2
2 1
1 2

Sample Output 1

1

Explanation for Sample 1

Only the student at position ~(2,2)~ will have their mark changed. All other students will keep their current mark. Thus, ~k_{1,1} = k_{1,2} = k_{2,1} = 0~, and ~k_{2,2} = 1~. The student at position ~(2,2)~ will have their marks changed by one due to ~a_{1,1} = 2~ ~(a_{1,1} \ge p_{2,2})~. The sum of all ~k_{i,j}~ is therefore one.

Sample Input 2

5
1 4 2 5 3
5 2 8 4 2
1 1 1 1 3
9 9 2 3 1
1 1 1 1 1

Sample Output 2

82

Sample Input 3

10
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
10 9 8 7 6 5 4 3 2 1
10 9 8 7 6 5 4 3 2 1
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
10 9 8 7 6 5 4 3 2 1
10 9 8 7 6 5 4 3 2 1
10 9 8 7 6 1 2 3 4 5
10 9 8 7 6 1 2 3 4 5

Sample Output 3

1420