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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分