CF1887F Minimum Segments

You had a sequence $ a_1, a_2, \ldots, a_n $ consisting of integers from $ 1 $ to $ n $ , not necessarily distinct. For some unknown reason, you decided to calculate the following characteristic of the sequence: - Let $ r_i $ ( $ 1 \le i \le n $ ) be the smallest $ j \ge i $ such that on the subsegment $ a_i, a_{i+1}, \ldots, a_j $ all distinct numbers from the sequence $ a $ appear. More formally, for any $ k \in [1, n] $ , there exists $ l \in [i, j] $ such that $ a_k = a_l $ . If such $ j $ does not exist, $ r_i $ is considered to be equal to $ n+1 $ . - The characteristic of the sequence $ a $ is defined as the sequence $ r_1, r_2, \ldots, r_n $ . Unfortunately, the sequence $ a $ got lost, but you still have its characteristic $ r $ . You want to reconstruct any sequence $ a $ that matches the characteristic, or determine that there is an error in the characteristic and such a sequence does not exist.

Each test consist of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The description of test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the length of the lost sequence $ a $ . The second line of each test case contains $ n $ integers $ r_1, r_2, \ldots, r_n $ ( $ i \le r_i \le n+1 $ ) — the characteristic of the lost sequence $ a $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output the following: - If there is no sequence $ a $ with the characteristic $ r $ , print "No". - Otherwise, print "Yes" on the first line, and on the second line, print any sequence of integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le n $ ) that matches the characteristic $ r $ . You can output "YES" and "NO" in any case (for example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as a positive answer).

In the first test case, the sequence $ a = [1, 2, 1] $ is suitable. The integers $ 1 $ and $ 2 $ appear on the subsegments $ [1, 2] $ and $ [2, 3] $ . In the second test case, it can be proved that there is no suitable sequence $ a $ .