Minimum Segments
本题没有可用的提交语言。
Description
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 $r_1, r_2, \ldots, r_n$.
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 $r$.
Input
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 $2 \cdot 10^5$.
Output
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 $r$.
5
3
2 3 4
5
2 3 5 4 6
1
1
3
1 3 4
8
3 6 6 6 8 9 9 9
Yes
1 2 1
No
Yes
1
No
Yes
1 3 5 3 5 1 1 3
Note
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 $a$.