MEXchange

A permutation of length $N$ is a sequence in which each integer from $1$ to $N$ appears exactly once. For example, $\left[ 2,3,1,5,4 \right]$ is a permutation, but $\left[ 1,2,2 \right]$ is not, because $2$ appears twice. Also, $\left[ 1,3,4 \right]$ has length $3$ but is not a permutation, because it contains $4$.

Given a permutation $A$ of length $N$, define the sequence $B$ as follows.

$B_i=\operatorname{MEX}\left( \{A_1,A_2,\cdots ,A_i\} \right)\ (1 \leq i \leq N)$

Given a sequence $B$ of length $N$, find the permutation $A$.

$\operatorname{MEX}\left( S \right)$ is the smallest positive integer not contained in the set $S$. For example, $\operatorname{MEX}\left(\{ 1,2,5 \}\right) =3$ and $\operatorname{MEX}\left(\{ 2,3,4 \}\right) =1$. Note that the $\operatorname{MEX}$ defined in this problem can never be $0$.

The first line contains the length $N$ of the permutation $A$. $\left( 3\leq N\leq 200\,000 \right)$

The second line contains $N$ integers $B_i$, separated by spaces, which are the elements of the sequence $B$. $\left( 1\leq B_i\leq N+1 \right)$

On the first line, print Yes if a permutation $A$ that produces $B$ exists, and No otherwise.

If it exists, print the elements of the permutation $A$ on the second line, separated by spaces. If there are multiple answers, print any of them.