Term Project

Every student who signed up for the 'Problem Solving' course this fall term has to carry out a term project. There is no limit on how many students a team may have. All of the students can even belong to the same team, leaving a single team. To form the teams, every student picks one student to work with. Only one pick is allowed. A student who wants to work alone may pick themselves.

Students $s_1, s_2, \ldots, s_r$ form one team in exactly two situations: $r = 1$ and $s_1$ picked $s_1$, or $s_1$ picked $s_2$, $s_2$ picked $s_3$, ..., $s_{r-1}$ picked $s_r$, and $s_r$ picked $s_1$.

For example, suppose a class has 7 students numbered 1 through 7 and the picks came out like this.

With these picks, (3) and (4, 7, 6) form teams. Students 1, 2, and 5 belong to no team.

Given the result of the picks, write a program that counts the students who belong to no project team.

The first line contains the number of test cases $T$. The first line of each test case contains the number of students $n$ ($2 \le n \le 100{,}000$). The second line lists the number that each student picked, in order from student $1$ to student $n$. Students are numbered $1$ through $n$.

For each test case, print on one line the number of students who ended up on no project team.