Problem B

Statement
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Description:
This is an interactive problem.

Vasya and Petya are going to play the following game: Petya has some positive integer number $$$a$$$. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers $$$(x, y)$$$. Petya will answer him:

- "x", if $$$(x \bmod a) \geq (y \bmod a)$$$.
- "y", if $$$(x \bmod a) < (y \bmod a)$$$.

We define $$$(x \bmod a)$$$ as a remainder of division $$$x$$$ by $$$a$$$.

Vasya should guess the number $$$a$$$ using no more, than 60 questions.

It's guaranteed that Petya has a number, that satisfies the inequality $$$1 \leq a \leq 10^9$$$.

Help Vasya playing this game and write a program, that will guess the number $$$a$$$.

Input Format:
None

Output Format:
None

Note:
In the first test, you should play $$$3$$$ games with Petya's numbers $$$1$$$, $$$2$$$ and $$$3$$$.

In the first game, Petya will answer "x" (without quotes) to any question, because $$$(x \bmod 1) = 0$$$ for any integer $$$x$$$.

In the second game, if you will ask pair $$$(0, 0)$$$, the answer will be "x" (without quotes), because $$$(0 \bmod 2) \geq (0 \bmod 2)$$$. But if you will ask pair $$$(2, 5)$$$, the answer will be "y" (without quotes), because $$$(2 \bmod 2) < (5 \bmod 2)$$$, because $$$(2 \bmod 2) = 0$$$ and $$$(5 \bmod 2) = 1$$$.