Problem Statement

A sequence of positive integers $T=(T_1,T_2,\dots,T_M)$ of length $M$ is a palindrome if and only if $T_i=T_{M-i+1}$ for each $i=1,2,\dots,M$.

You are given a sequence of non-negative integers $A = (A_1,A_2,\dots,A_N)$ of length $N$. Determine if there is a sequence of positive integers $S=(S_1,S_2,\dots,S_N)$ of length $N$ that satisfies the following condition, and if it exists, find the lexicographically smallest such sequence.

• For each $i=1,2,\dots,N$, both of the following hold:
• The sequence $(S_{i-A_i},S_{i-A_i+1},\dots,S_{i+A_i})$ is a palindrome.
  • If $2 \leq i-A_i$ and $i+A_i \leq N-1$, the sequence $(S_{i-A_i-1},S_{i-A_i},\dots,S_{i+A_i+1})$ is not a palindrome.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq A_i \leq \min\{i-1,N-i\}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

If there is no sequence $S$ that satisfies the condition, print No.

If there is a sequence $S$ that satisfies the condition, let $S'$ be the lexicographically smallest such sequence and print it in the following format:

Yes
S'_1 S'_2 \dots S'_N