Report BST Keys in a Range

Source: Phuoc Hung OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Build a BST from $a_1,a_2,\ldots,a_n$ in insertion order. Duplicate keys are ignored.

Given integers $L$ and $R$, if $L\le R$, select every stored key $v$ satisfying $L\le v\le R$ and print the selected keys in increasing order.

If $L>R$, the requested range is considered empty and no key is selected.

Input

The first line contains $n$.

If $n>0$, the next line contains $n$ signed integers $a_1,a_2,\ldots,a_n$. If $n=0$, this line is absent.

The last line contains $L$ and $R$.

Output

If at least one key belongs to the closed interval $[L,R]$, print those keys in increasing order, separated by one space.

If no key qualifies or $L>R$, print EMPTY.

Subtasks

Subtask 1 (20 points): $0\le n\le 20$.

Subtask 2 (30 points): $0\le n\le 5000$.

Subtask 3 (50 points): $0\le n\le 200000$.

In all subtasks, $a_i,L,R$ are signed 64-bit integers. Duplicate insertion keys are ignored.

Examples

Input

7
8 3 10 1 6 14 4
4 10

Output

4 6 8 10

Explanation

The stored keys in the closed interval $[4,10]$ are $4,6,8,10$. In increasing order they are exactly 4 6 8 10.