Problem E
Ríkjafræði
Languages
en
is
Jörmunrekur spent his easter vacation reading up on a math subject known as category theory. It uses a lot of arrow diagrams to visualize the material. These diagrams display categories which consist of objects and arrows between objects. An important property of many of these diagrams is that they are commutative. That means that if you start at some object $A$ and follow some sequence of arrows to object $B$ the result is the same no matter which path you take. Jörmunrekur is taking a look at a particular diagram and wondering whether it is commutative. In this diagram each object is the usual three dimensional space and each arrow is a translation of that space. The arrows are given in the format $(x, y, z)$ which means that each point is translated by $x$ in the $x$-direction, by $y$ in the $y$-direction and by $z$ in the $z$-direction.
Input
The inputs begins with a line with two integers $1 \leq n \leq 10^5$ and $1 \leq m \leq 10^5$ where $n$ is the number of objects and $m$ is the number of arrows. The objects are numbered from $1$ to $n$. Next there are $m$ lines, each with $5$ integers $1 \leq a, b \leq n$, $-10^9 \leq x, y, z, \leq 10^9$. This denotes that in the diagram there is an arrow from object $a$ to object $b$ which denotes the translation $(x, y, z)$. Note that since each arrow corresponds to a bijective map there is also implicitly an arrow from $b$ to $a$ translating by $(-x, -y, -z)$.
Output
Print Jebb if the diagram is commutative, otherwise print Neibb.
Scoring
Group |
Points |
Constraints |
1 |
50 |
$1 \leq n \leq 200$ |
2 |
50 |
No further constraints |
Explanation of Sample Input
In the first sample there are two paths from $1$ to $4$. No matter which path is followed
the total translation is $(1, 1,
1)$ so the diagram is commutative.
In the second sample a new arrow has been added. If we
travel backwards along it from $1$ to $4$ the translation is $(-1,-1,-1)$ which is not the same as
for the other paths. Thus this diagram is not
commutative.
Sample Input 1 | Sample Output 1 |
---|---|
4 4 1 2 1 0 0 2 4 0 1 1 1 3 1 0 1 3 4 0 1 0 |
Jebb |
Sample Input 2 | Sample Output 2 |
---|---|
4 5 1 2 1 0 0 2 4 0 1 1 1 3 1 0 1 3 4 0 1 0 4 1 1 1 1 |
Neibb |