Habitat 
Time limit:  1.00 s 
Memory limit:  512 MB 

Uolevi has gotten a new job at a wildlife reserve.
The reserve can be represented as an $n \times n$ rectangle. Every position $(x, y)$ has a humidity bound $b_{(x, y)}$. We call a position $(x, y)$
muddy if:
 $b_{(x, y)} > k$
 There exists a position $(x_{\#}, y_{\#})$, such that $b_{(x_{\#}, y_{\#})} \leq k$, and $\leftx  x_{\#}\right + \lefty  y_{\#}\right \leq k$
where $k$ is the humidity constant for the reserve.
Uolevi's first task is to calculate the amount of habitable area for hippoes at the park. Since hippoes like mud, this is equal to the amount of muddy positions. However, he doesn't know the humidity constant for the reserve.
Can you calculate the amount of muddy positions for every humidity constant $k \in [0, n^{2}]$. Can you help him with this task?
Input
The first line of input contains the integer $n$: The size of the reserve.
After this, $n$ lines follow, each containing $n$ integers. The $x$'th integer on the $y$'th line is $b_{(x, y)}$.
Output
Output the number of muddy positions $(x, y)$ for every $k \in [0, n^{2}]$
Constraints
 $1 \leq n \leq 100$
 $1 \leq b_{(x, y)} \leq n^{2}$
Example
Input:
2
1 4
2 3
Output:
0 2 2 1 0