Triangle Validator and Area Calculator

Given three line segment lengths a, b, and c, determine whether they can form a triangle. A triangle can be formed if and only if the following conditions hold:

\( a + b > c, \quad a + c > b, \quad b + c > a \)

If the segments can form a triangle, compute its area using Heron's formula:

\( s = \frac{a+b+c}{2} \quad \text{and} \quad \text{Area} = \sqrt{s(s-a)(s-b)(s-c)} \)

If they cannot form a triangle, output No solution. (note the period at the end).

inputFormat

The input consists of a single line containing three numbers a, b, and c separated by spaces.

outputFormat

If the input lengths can form a triangle, output its area computed by Heron's formula. Otherwise, output No solution.

sample

3 4 5

6.0