CF1530D.Secret Santa

Every December, VK traditionally holds an event for its employees named "Secret Santa". Here's how it happens.

$n$ employees numbered from $1$ to $n$ take part in the event. Each employee $i$ is assigned a different employee $b_i$ , to which employee $i$ has to make a new year gift. Each employee is assigned to exactly one other employee, and nobody is assigned to themselves (but two employees may be assigned to each other). Formally, all $b_i$ must be distinct integers between $1$ and $n$ , and for any $i$ , $b_i \ne i$ must hold.

The assignment is usually generated randomly. This year, as an experiment, all event participants have been asked who they wish to make a gift to. Each employee $i$ has said that they wish to make a gift to employee $a_i$ .

Find a valid assignment $b$ that maximizes the number of fulfilled wishes of the employees.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 10^5$ ). Description of the test cases follows.

Each test case consists of two lines. The first line contains a single integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ) — the number of participants of the event.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le n$ ; $a_i \ne i$ ) — wishes of the employees in order from $1$ to $n$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, print two lines.

In the first line, print a single integer $k$ ( $0 \le k \le n$ ) — the number of fulfilled wishes in your assignment.

In the second line, print $n$ distinct integers $b_1, b_2, \ldots, b_n$ ( $1 \le b_i \le n$ ; $b_i \ne i$ ) — the numbers of employees assigned to employees $1, 2, \ldots, n$ .

$k$ must be equal to the number of values of $i$ such that $a_i = b_i$ , and must be as large as possible. If there are multiple answers, print any.

In the first test case, two valid assignments exist: $[3, 1, 2]$ and $[2, 3, 1]$ . The former assignment fulfills two wishes, while the latter assignment fulfills only one. Therefore, $k = 2$ , and the only correct answer is $[3, 1, 2]$ .