You are given a 0indexed 2D integer array peaks
where peaks[i] = [x_{i}, y_{i}]
states that mountain i
has a peak at coordinates (x_{i}, y_{i})
. A mountain can be described as a rightangled isosceles triangle, with its base along the x
axis and a right angle at its peak. More formally, the gradients of ascending and descending the mountain are 1
and 1
respectively.
A mountain is considered visible if its peak does not lie within another mountain (including the border of other mountains).
Return the number of visible mountains.
Example 1:
Input: peaks = [[2,2],[6,3],[5,4]]
Output: 2
Explanation: The diagram above shows the mountains.
 Mountain 0 is visible since its peak does not lie within another mountain or its sides.
 Mountain 1 is not visible since its peak lies within the side of mountain 2.
 Mountain 2 is visible since its peak does not lie within another mountain or its sides.
There are 2 mountains that are visible.
Example 2:
Input: peaks = [[1,3],[1,3]]
Output: 0
Explanation: The diagram above shows the mountains (they completely overlap).
Both mountains are not visible since their peaks lie within each other.
Constraints:
1 <= peaks.length <= 10^{5}
peaks[i].length == 2
1 <= x_{i}, y_{i} <= 10^{5}

