Hello, codeforces!

Sorry for the long break, but the last weeks of holidays and the first weeks of academic year took my attention. I hope today's trick will make you forgive me. :P

I invented this trick a few years ago, but for sure I wasn't first, and some of you already know it. Let's consider the following **interactive** task. There are *n* (1 ≤ *n* ≤ 10^{5}) hidden integers *a*_{i}, each of them from range [1, 10^{18}]. You are allowed to ask at most 103000 queries. In one query you can choose two integers *x* and *y* (1 ≤ *x* ≤ *n*, 1 ≤ *y* ≤ 10^{18}) and ask a question ''Is *a*_{x} ≥ *y*?'' The task is to find the value of the greatest element in the hidden array. The checker **isn't** adaptive.

Unfortunately, this task is only theoretical, and you cannot solve it anywhere, but it'll turn out, that solution can be handy in many other, much more complicated problems.