CF1007C.Guess two numbers

This is an interactive problem.

Vasya and Vitya play a game. Vasya thought of two integers $a$ and $b$ from $1$ to $n$ and Vitya tries to guess them. Each round he tells Vasya two numbers $x$ and $y$ from $1$ to $n$. If both $x=a$ and $y=b$ then Vitya wins. Else Vasya must say one of the three phrases:

1. $x$ is less than $a$;
2. $y$ is less than $b$;
3. $x$ is greater than $a$ or $y$ is greater than $b$.

Vasya can't lie, but if multiple phrases are true, he may choose any of them. For example, if Vasya thought of numbers $2$ and $4$, then he answers with the phrase $3$ to a query $(3, 4)$, and he can answer with the phrase $1$ or phrase $3$ to a query $(1, 5)$.

Help Vitya win in no more than $600$ rounds.

这是一个交互式问题。

瓦夏和维佳在玩一个游戏。瓦夏心中想好了两个整数 $a$ 和 $b$（均在 $1$ 到 $n$ 之间），维佳尝试猜出它们。每一轮，维佳向瓦夏报出两个数 $x$ 和 $y$（均在 $1$ 到 $n$ 之间）。若 $x = a$ 且 $y = b$，则维佳获胜；否则，瓦夏必须从以下三种说法中选择其一作答：

1. $x$ 小于 $a$；
2. $y$ 小于 $b$；
3. $x$ 大于 $a$ 或 $y$ 大于 $b$。

瓦夏不能说谎，但当多个说法同时为真时，他可以任选其一回答。例如，若瓦夏想的数是 $2$ 和 $4$，那么对于查询 $(3, 4)$，他必须回答第 $3$ 种说法；而对于查询 $(1, 5)$，他既可回答第 $1$ 种说法，也可回答第 $3$ 种说法。

请帮助维佳在不超过 $600$ 轮内获胜。

The first line contains a single integer $n$ ($1 \leq n \leq 10^{18}$) — the upper limit of the numbers.

第一行包含一个整数 $n$（$1 \leq n \leq 10^{18}$）—— 数字的上限。

Let's analyze the sample test. The chosen numbers are $2$ and $4$. The interactor was given two instructions.

For the query $(4, 3)$, it can return $2$ or $3$. Out of the two instructions the second one is chosen, so the interactor returns $a^{23}_2=3$.

For the query $(3, 4)$, it can return only $3$.

For the query $(3, 3)$, it can return $2$ or $3$. Out of the two instructions the first one is chosen (since in case of equal values, the least number is preferred), so the interactor returns $a^{23}_1=2$.

For the query $(1, 5)$, it can return $1$ or $3$. Out of the two instructions the first one is chosen, so the interactor returns $a^{13}_1=1$.

In the fifth query $(2, 4)$, the numbers are guessed correctly, the player wins.

我们来分析样例测试。玩家选择的数字是 $2$ 和 $4$。交互器收到了两条指令。

对于查询 $(4, 3)$，交互器可返回 $2$ 或 $3$。在两条指令中选择了第二条，因此交互器返回 $a^{23}_2=3$。

对于查询 $(3, 4)$，交互器只能返回 $3$。

对于查询 $(3, 3)$，交互器可返回 $2$ 或 $3$。在两条指令中选择了第一条（因为在返回值相等时，优先选择较小的数），因此交互器返回 $a^{23}_1=2$。

对于查询 $(1, 5)$，交互器可返回 $1$ 或 $3$。在两条指令中选择了第一条，因此交互器返回 $a^{13}_1=1$。

在第五次查询 $(2, 4)$ 中，玩家正确猜出了这两个数，获胜。