Triangle Existence Checker

ArrayGeometryMath

Given an array of three integer numbers representing the lengths of the sides of a triangle, determine whether these sides can form a valid triangle. A set of three sides can form a triangle if the sum of the lengths of any two sides is greater than the length of the third side. The function must return 'Yes' if the sides can form a triangle and 'No' otherwise.

Example 1

Input

[
  3,
  4,
  5
]

Output

Yes

Explanation. 3 + 4 > 5, 4 + 5 > 3, and 3 + 5 > 4.

Example 2

Input

[
  1,
  2,
  3
]

Output

Explanation. 1 + 2 is not greater than 3.

Example 3

Input

[
  5,
  5,
  5
]

Output

Yes

Explanation. All side combinations sum to more than the third side.

Example 4

Input

[
  10,
  1,
  2
]

Output

Explanation. 10 is greater than 1 + 2, cannot form a triangle.

Example 5

Input

[
  7,
  6,
  10
]

Output

Yes

Explanation. All side combinations sum to more than the third side.

Follow-up: How would your solution change if you also had to determine the type of triangle (equilateral, isosceles, or scalene)?

Constraints:

All side lengths are positive integers.

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