Find the Hyper Spot to Lie Down In

Shift spent a year traveling the world in VR inside the metaverse. Tired from the trip, Shift booked a room for one night at a nearby Virtual Condo.

The rooms in the Virtual Condo form an $11$-dimensional hypercube of $N \times N \times N \times N \times N \times N \times N \times N \times N \times N \times N$ cells. Each cell is a unit cube of size $1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1$, parallel to the $x$, $y$, $z$, $u$, $v$, $w$, $r$, $s$, $t$, $o$, and $p$ axes. Each cell is identified by coordinates $\left(x,y,z,u,v,w,r,s,t,o,p\right)$ with $1 \le x,y,z,u,v,w,r,s,t,o,p \le N$.

The room is full of cargo that cannot be moved. Each cargo item is a single unit cell, and the cargo takes up space Shift could use to lie down. Shift has to find a place to lie down in this poor environment.

A place to lie down needs 2 or more empty cells in a row in a straight line. Shift can stretch out along that line. Shift can lie down in any of eleven directions, each parallel to one of the eleven axes. Shift always stretches fully, so the body always touches a wall or a cargo item. Shift never lies down halfway.

In the room shown in the picture above, there are $9\,765\,627$ places to lie down along the $x$ axis, $9\,765\,625$ along the $y$ axis, $9\,765\,625$ along the $z$ axis, $9\,765\,625$ along the $u$ axis, $9\,765\,625$ along the $v$ axis, $9\,765\,625$ along the $w$ axis, $9\,765\,624$ along the $r$ axis, $9\,765\,625$ along the $s$ axis, $9\,765\,625$ along the $t$ axis, $9\,765\,625$ along the $o$ axis, and $9\,765\,627$ along the $p$ axis.

Given the room size $N$ and the layout of the room, write a program that counts the places to lie down along each of the eleven axes.

The first line contains the room size $N$ and the number of obstacles $K$ ($0 \le K \le 111\,111$).

The next $K$ lines give the coordinates of the obstacles in the order $x$, $y$, $z$, $u$, $v$, $w$, $r$, $s$, $t$, $o$, $p$. No two or more obstacles occupy the same position.

On the first line, print the number of places to lie down along the $x$ axis.

On the second line, print the number of places to lie down along the $y$ axis.

On the third line, print the number of places to lie down along the $z$ axis.

On the fourth line, print the number of places to lie down along the $u$ axis.

On the fifth line, print the number of places to lie down along the $v$ axis.

On the sixth line, print the number of places to lie down along the $w$ axis.

On the seventh line, print the number of places to lie down along the $r$ axis.

On the eighth line, print the number of places to lie down along the $s$ axis.

On the ninth line, print the number of places to lie down along the $t$ axis.

On the tenth line, print the number of places to lie down along the $o$ axis.

On the eleventh line, print the number of places to lie down along the $p$ axis.