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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 $$$a_2, a_3, \ldots, a_n$$$ 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 $$$n$$$ ($$$2 \leq n \leq 100\,000$$$) — the length of the sequence $$$a$$$.

The second line contains $$$n$$$ distinct integers $$$a_i$$$ ($$$1 \leq a_i \leq 10^9$$$) — 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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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