A13695 | Rainbow Triples

You are given a sequence $a_1, a_2, \ldots, a_n$ of non-negative integers.

You need to find the largest number $m$ of triples $(i_1, j_1, k_1)$ , $(i_2, j_2, k_2)$ , ..., $(i_m, j_m, k_m)$ such that:

- $1 \leq i_p < j_p < k_p \leq n$ for each $p$ in $1, 2, \ldots, m$ ;
- $a_{i_p} = a_{k_p} = 0$ , $a_{j_p} \neq 0$ ;
- all $a_{j_1}, a_{j_2}, \ldots, a_{j_m}$ are different;
- all $i_1, j_1, k_1, i_2, j_2, k_2, \ldots, i_m, j_m, k_m$ are different.

The first line of input contains one integer $t$ ( $1 \leq t \leq 500\,000$ ): the number of test cases.

The first line of each test case contains one integer $n$ ( $1 \leq n \leq 500\,000$ ).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \leq a_i \leq n$ ).

The total sum of $n$ is at most $500\,000$ .

For each test case, print one integer $m$ : the largest number of proper triples that you can find.