Score: $600$ points

问题陈述

给定一个整数序列 $P=(P_1,P_2,\dots,P_N)$，它是从 $1$ 到 $N$ 的一个排列。

对于每个 $i=1,2,\dots,N$，打印出满足以下所有条件的整数对 $(l,r)$ 的最小值 $r-l+1$。如果不存在这样的 $(l,r)$，则打印 -1。

• $1 \leq l \leq i \leq r \leq N$
• $r-l+1$ 是奇数。
• 序列 $P$ 的连续子序列 $(P_l,P_{l+1},\dots,P_r)$ 的中位数 不是 $P_i$。

这里，对于长度为 $L$（奇数）的整数序列 $A$，$A$ 的中位数定义为将 $A$ 排序后得到的序列 $A'$ 的第 $\frac{L+1}{2}$ 个值。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

You are given a permutation $P=(P_1,P_2,\dots,P_N)$ of integers from $1$ to $N$.

For each $i=1,2,\dots,N$, print the minimum value of $r-l+1$ for a pair of integers $(l,r)$ that satisfies all of the following conditions. If no such $(l,r)$ exists, print -1.

• $1 \leq l \leq i \leq r \leq N$
• $r-l+1$ is odd.
• The median of the contiguous subsequence $(P_l,P_{l+1},\dots,P_r)$ of $P$ is not $P_i$.

Here, the median of $A$ for an integer sequence $A$ of length $L$ (odd) is defined as the $\frac{L+1}{2}$-th value of the sequence $A'$ obtained by sorting $A$ in ascending order.

Constraints

• $3 \leq N \leq 3 \times 10^5$
• $(P_1,P_2,\dots,P_N)$ is a permutation of integers from $1$ to $N$.
• All input values are integers.

Input

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

$N$

$P_1$ $P_2$ $\dots$ $P_N$

Output

Print the answers for $i=1,2,\dots,N$ in this order, separated by spaces.

Sample Input 1

5
1 3 5 4 2

Sample Output 1

3 3 3 5 3

For example, when $i=2$, if we set $(l,r)=(2,4)$, then $r-l+1=3$ is odd, and the median of $(P_2,P_3,P_4)=(3,5,4)$ is $4$, which is not $P_2$, so the conditions are satisfied. Thus, the answer is $3$.

On the other hand, when $i=4$, the median of $(P_l,\dots,P_r)$ for any of $(l,r)=(4,4),(2,4),(3,5)$ is $P_4=4$. If we set $(l,r)=(1,5)$, the median of $(P_1,P_2,P_3,P_4,P_5)=(1,3,5,4,2)$ is $3$, which is not $P_4$, so the conditions are satisfied. Thus, the answer is $5$.

Sample Input 2

3
2 1 3

Sample Output 2

-1 3 3

When $i=1$, no pair of integers $(l,r)$ satisfies the conditions.

Sample Input 3

14
7 14 6 8 10 2 9 5 4 12 11 3 13 1

Sample Output 3

5 3 3 7 3 3 3 5 3 3 5 3 3 3