Problem Statement

There are $N$ people, numbered from $1$ to $N$. Every person has $M$ types of ability parameters, and the parameter of ability $j$ of person $i$ is $R_{i,j}$.

A total of $N$ programming contests will be held. In the $k$-th contest, the $k$ people from person $1$ to person $k$ participate.

For each contest, the only people who have a possibility of winning are those who attain the maximum value among the participants in at least $1$ type of ability parameter. For each contest, determine how many people have a possibility of winning.

Input

$N$ $M$
$R_{1,1}$ $R_{1,2}$ ... $R_{1,M}$
$R_{2,1}$ $R_{2,2}$ ... $R_{2,M}$
:
$R_{N,1}$ $R_{N,2}$ ... $R_{N,M}$

The $1$-st line contains the number of people $N(1 \le N \le 10^5)$ and the number of types of ability parameters $M(1 \le M \le 10)$.

The $i$-th of the following $N$ lines contains $M$ space-separated integers $R_{i,j}(1 \le R_{i,j} \le 10^9)$, where the $j$-th value is the parameter of ability $j$ of person $i$.

Output

The output consists of $N$ lines. On the $i$-th line, print the number of people who have a possibility of winning the $i$-th contest.

Sample

5 1
5
4
5
6
7

1
1
2
1
1

7 3
1 2 3
3 1 2
1 2 1
3 3 4
1000000000 1000000000 1000000000
334 57 119
114 1333 514

1
2
3
2
1
1
1