Beginner's Bucket Sort

Problem Description

Little J has finally learned about arrays, and he knows that he can use an array to sort a sequence of numbers!

Today he gives it a try, using an array to sort $n$ numbers. Can you do it too?

Input Format

The first line contains a positive integer $n(0 \lt n \le 10^4)$.

The second line contains $n$ consecutive non-negative integers, each not greater than $10^4$.

Output Format

One line: output the $n$ numbers sorted from smallest to largest, separated by single spaces. If a number appears multiple times, write it only once in the sorted result.

Sample Input 1

5
3 7 0 2 4

Sample Output 1

0 2 3 4 7

Sample Input 2

5
1 2 1 2 1

Sample Output 2

1 2

Bucket Sort

By observation we find that the $n$ consecutive non-negative integers (each $\le 10^4$) are exactly suitable to be used as array indices.

So far we have only one way of using arrays:

a[i] = x; means the $i$-th number is $x$.

Now let's think: can we also use it the other way around?

c[x]=1; — what does that represent?

It means that $x$ appears $1$ time in array $a$.

We call the array $c$ a "bucket", used to record how many times a number appears in another array.

We let $i$ start from $0$ and loop until the maximum value among the inputs; as long as $c[i]$ is not $0$, we output $i$.

Special note: the size of the $c$ array depends on the maximum value among the inputs, and all input numbers must be natural numbers that can serve as array indices.