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문제

민혁이가 심시티 게임에서 플레이하고 있는 도시는 교통 정체가 상당히 심하다. 교통 정체는 게임을 플레이 할 수 없을 정도로 심해졌고, 민혁이는 엄청난 짜증을 느꼈다. 따라서, 민혁이는 새 도시를 시작하기로 결심했다.

이전 도시에서 교통 정체의 가장 큰 원인은 교차로였다. 교차로를 아무리 잘 설계해도, 게임 상의 AI 문제로 교통 정체는 피할 수 없는 선택이다. 교통 정체를 피하기 위해서는 교차로가 없는 도로를 만들면 된다. 

어떻게 교차로 없이 도시의 모든 곳을 방문할 수 있을까? 민혁이는 인터넷에서 열심히 살펴보다가 힐베르트 곡선을 찾았다. 힐베르트 곡선을 이용하면, 교차로 없이 도시를 만들 수 있을 것이다.

첫 번째 힐베르트 곡선은 컵(왼쪽 그림에 나와있는 ㄷ자) 하나로 이루어져 있다. 두 번째 힐베르트 곡선은 구역을 네 개의 정사각형으로 나누고, 각각의 정사각형에 컵을 채운 다음에 네 컵을 직선으로 연결한 것이다.

힐베르트 곡선에 대한 설명은 4645번에 잘 나와 있기 때문에, 이 문제를 참고하면 된다.

모든 모퉁이에는 집이 하나씩 있고, 순서대로 번호가 매겨져 있다. 가장 왼쪽 위에 있는 집이 1번이고, 인접한 두 집 사이의 거리는 10이다.

몇 번째 힐베르트 곡선인지와 두 집의 번호가 주어졌을 때, 두 집 사이의 거리를 구하는 프로그램을 작성하시오. 모든 주민은 헬리콥터를 가지고 있어서, 도로를 이용하지 않고 하늘을 날아서 이동한다. 헬리콥터의 이륙과 착륙하는데 필요한 거리는 무시하며, 항상 최단거리를 이용한다.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스는 한 줄로 이루어져 있고, 세 정수 n, h, o 가 주어진다. n은 마을의 도로가 n번째 힐베르트 곡선임을 나타내며, h와 o는 거리를 구해야 하는 두 집의 번호이다. (n < 16, h,o < 231)

출력

각 테스트 케이스에 대해서, 입력으로 주어진 두 집의 거리를 가까운 정수로 반올림해서 출력한다.

예제 입력 1

3
1 1 2
2 16 1
3 4 33

예제 출력 1

10
30
50
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(n &lt; 16, h,o &lt; 2<sup>31<\/sup>)<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \ub450 \uc9d1\uc758 \uac70\ub9ac\ub97c \uac00\uae4c\uc6b4 \uc815\uc218\ub85c \ubc18\uc62c\ub9bc\ud574\uc11c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5405","problem_lang":"1","title":"Fractal Streets","description":"<p>With a growing desire for modernization in our increasingly larger cities comes a need for new street designs. Chris is one of the unfortunate city planners responsible for these designs. Each year the demands keep increasing, and this year he has even been asked to design a completely new city.<\/p>\r\n\r\n<p>More work is not something Chris needs right now, since like any good bureaucrat, he is extremely lazy. Given that this is a character trait he has in common with most computer scientists it should come as no surprise that one of his closest friends, Paul, is in fact a computer scientist. And it was Paul who suggested the brilliant idea that has made Chris a hero among his peers: Fractal Streets! By using a Hilbert curve, he can easily fi ll in rectangular plots of arbitrary size with very little work.<\/p>\r\n\r\n<p>A Hilbert curve of order 1 consists of one &quot;cup&quot;. In a Hilbert curve of order 2 that cup is replaced by four smaller but identical cups and three connecting roads. In a Hilbert curve of order 3 those four cups are in turn replaced by four identical but still smaller cups and three connecting roads, etc. At each corner of a cup a driveway (with mailbox) is placed for a house, with a simple successive numbering. The house in the top left corner has number 1, and the distance between two adjacent houses is 10 m.<\/p>\r\n\r\n<p>The situation is shown graphically in gure 2. As you can see the Fractal Streets concept successfully eliminates the need for boring street grids, while still requiring very little effort from our bureaucrats.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/hb.png\" style=\"height:227px; width:587px\" \/><\/p>\r\n\r\n<p>Figure 2: Hilbert curves of order 1, 2 and 3, with the location of the houses indicated.<\/p>\r\n\r\n<p>As a token of their gratitude, several mayors have offered Chris a house in one of the many new neighborhoods built with his own new scheme. Chris would now like to know which of these offerings will get him a house closest to the local city planning o\u000ece (of course each of these new neighborhoods has one). Luckily he will not have to actually drive along the street, because his new company &quot;car&quot; is one of those new flying cars. This high-tech vehicle allows him to travel in a straight line from his driveway to the driveway of his new o\u000ece. Can you write a program to determine the distance he will have to y for each offer (excluding the vertical distance at takeoff and landing)?<\/p>\r\n","input":"<p>On the fi rst line of the input is a positive integer, the number of test cases. Then for each testcase:<\/p>\r\n\r\n<ul>\r\n\t<li>A line containing a three positive integers, n &lt; 16 and h, o &lt; 2<sup>31<\/sup>, specifying the order of the Hilbert curve, and the house numbers of the offered house and the local city planning office.<\/li>\r\n<\/ul>\r\n","output":"<p>For each test case:<\/p>\r\n\r\n<ul>\r\n\t<li>One line containing the distance Chris will have to y to his work in meters, rounded to the nearest integer.<\/li>\r\n<\/ul>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]