Fixed-Length Binary Conversion

You are given n house numbers. Each house number is a non‐negative integer and is guaranteed to satisfy \(0 \leq a_i < 1024\). Your task is to convert each house number into its binary representation. The length of the binary string should be equal to the number of bits required to represent the maximum house number in the list. For numbers with a binary representation shorter than this length, add leading zeros.

Note: If the maximum number is 0, its binary representation should be "0" without any additional leading zeros.

For example, given the numbers [3, 7, 2, 15, 6], the maximum is 15 whose binary representation is 4 bits long. Therefore, the binary representation for 3 is converted to "0011" (with leading zeros added as necessary).

It is guaranteed that input house numbers are within the allowed range.

inputFormat

The input is given in the following format from standard input (stdin):

The first line contains a single integer n, which is the number of house numbers.
The second line contains n space-separated integers representing the house numbers in decimal format.

It is guaranteed that \(0 \leq a_i < 1024\).

outputFormat

Print the fixed-length binary representations in order, each on a separate line. The length of each binary number must be equal to the number of bits in the binary representation of the maximum number given in the input.

## sample

5
3 7 2 15 6

0011
0111
0010
1111
0110

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