Score: $625$ points

问题陈述

一个正整数序列 $T=(T_1,T_2,\dots,T_M)$ 的长度为 $M$，如果且仅如果对于每个 $i=1,2,\dots,M$，都有 $T_i=T_{M-i+1}$，则称其为一个回文序列。

给定一个非负整数序列 $A = (A_1,A_2,\dots,A_N)$ 的长度为 $N$。确定是否存在一个正整数序列 $S=(S_1,S_2,\dots,S_N)$ 的长度为 $N$，满足以下条件，如果存在，找到字典序最小的这样一个序列。

• 对于每个 $i=1,2,\dots,N$，以下两个条件都成立：
  • 序列 $(S_{i-A_i},S_{i-A_i+1},\dots,S_{i+A_i})$ 是一个回文序列。
  • 如果 $2 \leq i-A_i$ 且 $i+A_i \leq N-1$，序列 $(S_{i-A_i-1},S_{i-A_i},\dots,S_{i+A_i+1})$ 不是一个回文序列。

以上为大语言模型 kimi 翻译，仅供参考。

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

$S'_1$ $S'_2$ $\dots$ $S'_N$

Sample Input 1

7
0 0 2 0 2 0 0

Sample Output 1

Yes
1 1 2 1 1 1 2

$S = (1,1,2,1,1,1,2)$ satisfies the condition:

• $i=1$: $(A_1)=(1)$ is a palindrome.
• $i=2$: $(A_2)=(1)$ is a palindrome, but $(A_1,A_2,A_3)=(1,1,2)$ is not.
• $i=3$: $(A_1,A_2,\dots,A_5)=(1,1,2,1,1)$ is a palindrome.
• $i=4$: $(A_4)=(1)$ is a palindrome, but $(A_3,A_4,A_5)=(2,1,1)$ is not.
• $i=5$: $(A_3,A_4,\dots,A_7)=(2,1,1,1,2)$ is a palindrome.
• $i=6$: $(A_6)=(1)$ is a palindrome, but $(A_5,A_6,A_7)=(1,1,2)$ is not.
• $i=7$: $(A_7)=(2)$ is a palindrome.

There are other sequences like $S=(2,2,1,2,2,2,1)$ that satisfy the condition, but print the lexicographically smallest one, which is $(1,1,2,1,1,1,2)$.

Sample Input 2

7
0 1 2 3 2 1 0

Sample Output 2

Yes
1 1 1 1 1 1 1

Sample Input 3

7
0 1 2 0 2 1 0

Sample Output 3

No