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