A_A_i

AtCoder

IDarc209_d

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $A = (A_1, A_2, \ldots, A_N)$ of length $N$. Each element is either an integer between $1$ and $N$ (inclusive) or $-1$. Snuke has decided to create a new sequence using this sequence $A$. First, replace all $-1$s in this sequence $A$ with integers between $1$ and $N$ (inclusive). Next, create a sequence $B = (B_1, B_2, \ldots, B_N)$ of length $N$ according to the following formula: * $B_i=A_{A_i}$ Find the lexicographically smallest possible sequence $B$. You are given $T$ test cases. Solve each of them. What is the lexicographical order of sequences?A sequence $C = (C_1,C_2,\ldots,C_N)$ is **lexicographically smaller** than a sequence $D = (D_1,D_2,\ldots,D_N)$ if and only if there exists an integer $1 \leq i \leq N$ such that both of the following hold: * $(C_1,C_2,\ldots,C_{i-1}) = (D_1,D_2,\ldots,D_{i-1})$ * $C_i$ is (numerically) smaller than $D_i$. ## Constraints * $1 \le T \le 10^5$ * $1 \le N \le 5 \times 10^5$ * $1 \le A_i \le N$ or $A_i = -1$. * The sum of $N$ over all test cases is at most $5\times 10^5$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $T$ $case_1$ $case_2$ $\vdots$ $case_T$ Each case is given in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

3
4
4 -1 -1 3
5
5 4 5 3 1
7
-1 6 5 -1 7 -1 6

Output #1

3 1 4 1
1 3 1 5 5
1 1 7 1 6 1 1

In the first test case, the sequence $A$ before Snuke's replacement is $(4,-1,-1,3)$.
Suppose he replaces it to get $A=(4, 3, 1, 3)$.
Then, $B=(A_4, A_3, A_1, A_3)=(3, 1, 4, 1)$.
It is impossible to obtain a lexicographically smaller sequence $B$ than this.

API Response (JSON)

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