Turf Wars

There are $N$ gangs in a city. Each gang occupies several rectangular territories, and any overlap between territories of different gangs causes a dispute.

$N$ satisfies $2 \le N \le 300$, and gang $i$ owns $M_i$ territories. Every territory is a rectangle whose sides are parallel to the $x$ and $y$ axes, given by its lower-left corner $(x_1, y_1)$ and its upper-right corner $(x_2, y_2)$. The coordinates are integers satisfying $0 \le x_1 < x_2 < 1000000$ and $0 \le y_1 < y_2 < 1000000$.

A dispute region is a part where two territories of different gangs overlap with positive area. Territories that meet only along an edge or at a point are not a dispute region.

Each gang must give up exactly one of its $M_i$ territories. Decide whether all dispute regions can be eliminated this way.

The first line contains the number of gangs $N$.

Then the territories of gang $1$ through gang $N$ follow in order. The first line for gang $i$ contains the number of territories $M_i$ ($2 \le M_i \le 15$). Each of the following $M_i$ lines contains $x_1$, $y_1$, $x_2$, $y_2$, the coordinates of the lower-left and upper-right corners of one territory, separated by spaces.

Territories owned by one gang never overlap each other.

If the gangs can eliminate every dispute region by each giving up one territory, print YES. Otherwise, print NO.

If one territory overlaps two different territories of another gang, it can never be kept and must be given up. Conversely, every territory overlapping a kept territory must be given up, so a single choice can force the choices of other gangs in a chain.