Game

Jian-Jia is a young boy who loves playing games. When he is asked a question, he prefers playing games rather than answering directly. Jian-Jia met his friend Mei-Yu and told her about the flight network in Taiwan. There are $n$ cities in Taiwan (numbered from $0$ to n - 1), some of which are connected by flights. Each flight connects two cities and can be taken in both directions.

Mei-Yu asked Jian-Jia whether it is possible to go between any two cities by plane (either directly or indirectly). Jian-Jia did not want to reveal the answer, but instead suggested to play a game. Mei-Yu can ask him questions of the form "Are cities $x$ and $y$ directly connected with a flight?", and Jian-Jia will answer such questions immediately. Mei-Yu will ask about every pair of cities exactly once, giving r = n \cdot (n - 1) / 2 questions in total. Mei-Yu wins the game if, after obtaining the answers to the first $i$ questions for some i < r, she can infer whether or not it is possible to travel between every pair of cities by flights (either directly or indirectly). Otherwise, that is, if she needs all $r$ questions, then the winner is Jian-Jia.

In order for the game to be more fun for Jian-Jia, the friends agreed that he may forget about the real Taiwanese flight network, and invent the network as the game progresses, choosing his answers based on Mei-Yu's previous questions. Your task is to help Jian-Jia win the game, by deciding how he should answer the questions.

Example

We explain the game rules with three examples. Each example has n = 4 cities and r = 6 rounds of question and answer.

In the first example (the following table), Jian-Jia loses because after round $4$, Mei-Yu knows for certain that one can travel between any two cities by flights, no matter how Jian-Jia answers questions $5$ or $6$.

In the next example Mei-Yu can prove after round $3$ that no matter how Jian-Jia answers questions $4$, $5$ or $6$, one cannot travel between cities $0$ and $1$ by flights, so Jian-Jia loses again.

In the final example Mei-Yu cannot determine whether one can travel between any two cities by flights until all six questions are answered, so Jian-Jia wins the game. Specifically, because Jian-Jia answered yes to the last question (in the following table), then it is possible to travel between any pair of cities. However, if Jian-Jia had answered no to the last question instead then it would be impossible.

Task

Please write a program that helps Jian-Jia win the game. Note that neither Mei-Yu nor Jian-Jia knows the strategy of each other. Mei-Yu can ask about pairs of cities in any order, and Jian-Jia must answer them immediately without knowing the future questions. You need to implement the following two functions.

• initialize($n$) - We will call your initialize first. The parameter $n$ is the number of cities.

• hasEdge($u$, $v$) - Then we will call hasEdge for r = n \cdot (n - 1) / 2 times. These calls represent Mei-Yu's questions, in the order that she asks them. You must answer whether there is a direct flight between cities $u$ and $v$. Specifically, the return value should be $1$ if there is a direct flight, or $0$ otherwise.

Scoring

Each subtask consists of several games. You will only get points for a subtask if your program wins all of the games for Jian-Jia.

Implementation details

You have to implement the subprograms described above using the following signatures:

C/C++ programs

• void initialize(int n);

• int hasEdge(int u, int v);

Pascal programs

• procedure initialize(n: longint);

• function hasEdge(u, v: longint): longint;