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문제

ACM(Advanced Chip Manufacture)이라는 회사의 수석 칩(chip) 설계자인 한승이는 고민에 빠져있다. 경로 설계자들의 잘못으로 두 개의 블럭의 포트를 연결하는 칩 위의 시그널들이 서로 교차하게 만들어졌다. 이 시점에서 경로 설계를 다시 하는 것은 비용이 너무 많이든다. 그 대신 엔지이너들은 교차하는 시그널들을 브리징 하기로 했다. 브리징은 시그널이 서로 교차하는 경우 하나의 시그널이 다른 시그널과 접촉하지 않도록 수직으로 띄우는 작업이다. 하지만 브리징은 어려운 작업이므로 가능하면 적은 수의 시그널만 브리징 해야한다. 실리콘 표면에서 서로 교차하지 않고 연결될 수 있는 최대 시그널의 개수를 찾는 프로그램을 작성하시오.

 

그림 1. 문제가 생긴 두 개의 블럭의 포트와 포트를 연결하는 시그널 그림 2. 최대 세 개의 시그널이 서로 교차하지 않고 연결될 수 있다. 점선으로 표시된 시그널은 브리징 해야한다.

 

두 개의 블럭의 포트는 1번부터 N번까지 위에서 아래로 번호가 매겨져 있다. 각 포트는 다른 블록의 한 포트와 연결된다.

입력

입력의 첫 줄에는 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스는 첫 번째 줄에 포트의 개수 N(1 ≤ N ≤ 40000)이 주어지고, 두 번째 줄부터는 왼쪽 블럭의 포트와 연결되어야 하는 오른쪽 블럭의 포트 번호 ki(1 ≤ ki ≤ N)가 한 줄에 하나씩 N개 주어진다. 즉, i+1번째 줄에는 왼쪽 블럭의 i번 포트와 연결되어야 하는 오른쪽 블럭의 포트 번호가 주어진다.

출력

각 테스트 케이스에 대해 서로 교차하지 않고 연결될 수 있는 최대 시그널의 개수를 한 줄에 하나씩 출력한다.

예제 입력 1

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10
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1
9
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9
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1
7
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6

예제 출력 1

3
9
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Once more the routing designers have screwed up completely, making the signals on the chip connecting the ports of two functional blocks cross each other all over the place. At this late stage of the process, it is too expensive to redo the routing. Instead, the engineers have to bridge the signals, using the third dimension, so that no two signals cross. However, bridging is a complicated operation, and thus it is desirable to bridge as few signals as possible. The call for a computer program that finds the maximum number of signals which may be connected on the silicon surface without crossing each other, is imminent. Bearing in mind that there may be thousands of signal ports at the boundary of a functional block, the problem asks quite a lot of the programmer. Are you up to the task?<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/bridingsignal.png\" style=\"height:225px; width:532px\" \/><\/p>\r\n\r\n<p>Figure 1. To the left: The two blocks&#39; ports and their signal mapping (4,2,6,3,1,5). To the right: At most three signals may be routed on the silicon surface without crossing each other. The dashed signals must be bridged.<\/p>\r\n\r\n<p>A typical situation is schematically depicted in figure 1. The ports of the two functional blocks are numbered from 1 to p, from top to bottom. The signal mapping is described by a permutation of the numbers 1 to p in the form of a list of p unique numbers in the range 1 to p, in which the i:th number specifies which port on the right side should be connected to the i:th port on the left side. Two signals cross if and only if the straight lines connecting the two ports of each pair do.<\/p>\r\n","input":"<p>On the first line of the input, there is a single positive integer n, telling the number of test scenarios to follow. Each test scenario begins with a line containing a single positive integer p&lt;40000, the number of ports on the two functional blocks. Then follow p lines, describing the signal mapping: On the i:th line is the port number of the block on the right side which should be connected to the i:th port of the block on the left side.<\/p>\r\n","output":"<p>For each test scenario, output one line containing the maximum number of signals which may be routed on the silicon surface without crossing each other.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]