Maximal Points

Problem Description

On a plane, consider two points $(x,y)$ and $(a,b)$. We say that $(x,y)$ dominates $(a,b)$ if $x \ge a$ and $y \ge b$.

Graphically, this means that $(a,b)$ lies in the infinite region whose upper-right corner is $(x,y)$.

Given a set of $n$ points, there always exist some points that are not dominated by any point in the set; these are called the maximal points.

Write a program to find all maximal points and output their coordinates in increasing order of the $x$-coordinate.

This problem guarantees: $n \le 100$, and no point has a negative coordinate.

Input Format

The input consists of two lines.

The first line is a positive integer $n$, the number of points.

The second line contains the coordinates of the $n$ points. All coordinate values are integers in the range $0$ to $100$, and no two points in the input have the same coordinates.

Output Format

Output all maximal points in increasing order of the $x$-coordinate.

The output format is: $(x_1,y_1),(x_2,y_2),...(x_k,y_k)$.

Note: consecutive points are separated by a ,, and there is no , after the last point. Outputting too few or too many points will be judged wrong.

Sample Input 1

5 
1 2 2 2 3 1 2 3 1 4

Sample Output 1

(1,4),(2,3),(3,1)

Hint

Constraints

1s, 1024KiB for each test case.