The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 110 (Div. 2) |
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Finished |

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brute force

*800

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A. Game Outcome

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputSherlock Holmes and Dr. Watson played some game on a checkered board *n* × *n* in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.

For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8 + 3 + 6 + 7 = 24, sum of its row numbers equals 9 + 5 + 3 + 2 = 19, and 24 > 19.

Input

The first line contains an integer *n* (1 ≤ *n* ≤ 30). Each of the following *n* lines contain *n* space-separated integers. The *j*-th number on the *i*-th line represents the number on the square that belongs to the *j*-th column and the *i*-th row on the board. All number on the board are integers from 1 to 100.

Output

Print the single number — the number of the winning squares.

Examples

Input

1

1

Output

0

Input

2

1 2

3 4

Output

2

Input

4

5 7 8 4

9 5 3 2

1 6 6 4

9 5 7 3

Output

6

Note

In the first example two upper squares are winning.

In the third example three left squares in the both middle rows are winning:

5 7 8 4

9 5 3 2

1 6 6 4

9 5 7 3

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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