Line Reflection

medium

Given n points on a 2D plane, find if there is such a line parallel to y-axis that reflect the given points symmetrically, in other words, answer whether or not if there exists a line that after reflecting all points over the given line the set of the original points is the same that the reflected ones.

Note that there can be repeated points.

&lt;b&gt;Example 1:&lt;/b&gt;
&lt;img alt="" src="https://assets.leetcode.com/uploads/2020/04/23/356_example_1.PNG" style="width: 389px; height: 340px;"&gt;

Input: points = [[1,1],[-1,1]]
Output: true
Explanation: We can choose the line x = 0.

&lt;b&gt;Example 2:&lt;/b&gt;
&lt;img alt="" src="https://assets.leetcode.com/uploads/2020/04/23/356_example_2.PNG" style="width: 300px; height: 294px;"&gt;

Input: points = [[1,1],[-1,-1]]
Output: false
Explanation: We can't choose a line.

Input Format

Input is managed for you

Output Format

Output is managed for you

Constraints

n == points.length
1 &lt;= n &lt;= 10^4
-10^8 &lt;= points[i][j] &lt;= 10^8

Notice

Follow up:
Could you do better than O(n2) ?

Example

Input

Output

false

Pairs Of Non Coinciding Points

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