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D. Tree Construction

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputDuring the programming classes Vasya was assigned a difficult problem. However, he doesn't know how to code and was unable to find the solution in the Internet, so he asks you to help.

You are given a sequence *a*, consisting of *n* distinct integers, that is used to construct the binary search tree. Below is the formal description of the construction process.

- First element
*a*_{1}becomes the root of the tree. - Elements
*a*_{2},*a*_{3}, ...,*a*_{n}are added one by one. To add element*a*_{i}one needs to traverse the tree starting from the root and using the following rules:- The pointer to the current node is set to the root.
- If
*a*_{i}is greater than the value in the current node, then its right child becomes the current node. Otherwise, the left child of the current node becomes the new current node. - If at some point there is no required child, the new node is created, it is assigned value
*a*_{i}and becomes the corresponding child of the current node.

Input

The first line of the input contains a single integer *n* (2 ≤ *n* ≤ 100 000) — the length of the sequence *a*.

The second line contains *n* distinct integers *a*_{i} (1 ≤ *a*_{i} ≤ 10^{9}) — the sequence *a* itself.

Output

Output *n* - 1 integers. For all *i* > 1 print the value written in the node that is the parent of the node with value *a*_{i} in it.

Examples

Input

3

1 2 3

Output

1 2

Input

5

4 2 3 1 6

Output

4 2 2 4

Note

Picture below represents the tree obtained in the first sample.

Picture below represents the tree obtained in the second sample.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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