Frequency Counter and Mode Finder

You are given a list of n integers. Your task is to compute two things:

• A frequency dictionary that counts how many times each unique integer appears. The dictionary should be output in sorted order (increasing numerical order of the keys).
• The integer that appears most frequently. In the event of a tie, choose the smallest integer among those.

Mathematically, let the frequency of an integer x be denoted by \(f(x)\). Then the mode is defined as the integer m such that $$ \begin{aligned} m = \min\{x \mid f(x) = \max_{y}f(y)\} \end{aligned} $$

Your program should read input from stdin and output the results to stdout as described in the Input/Output sections.

inputFormat

The first line contains an integer n, representing the number of integers. The second line contains n space-separated integers.

Example:

4
1 2 3 4

outputFormat

The output consists of two lines:

• The first line displays the frequency dictionary. For each unique integer, output the key and its count in the format key:count separated by a single space. The keys must be in increasing order.
• The second line displays the most frequent integer (if there is a tie, the smallest among them).

Example:

1:1 2:1 3:1 4:1
1

## sample

1
1

1:1
1

</p>