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 $r$.