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Maximum Height Tree
Easy Accuracy: 33.49% Submissions: 120 Points: 2

Given N dots that form a triangle such that ith line contains i number of dots.

    .
   . .
  . . .
 . . . .

Find the minimum hieght H of the triangle that can be formed using these N dots.

 

Example 1:

Input: N = 1
Output: 2
Explaination: The height will be 1. We 
need one dot to create first line. With 
the remaining one we cannot complete the 
second line.

 

Example 2:

Input: N = 10
Output: 4
Explaination: With 10 dots we can complete 
total four lines. The layers will have 1, 
2, 3 and 4 dots respectively.

 

Your Task:
You do not need to read input or print anything. Your task is to complete the function height() which takes N as input parameter and returns the height of the triangle that we can form using N dots.

 

Expected Time Comlpexity: O(1)
Expected Auxiliary Space: O(1)

 

Constraints:
1 ≤ N ≤ 105  

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