Based on the filename "2017a.t" and common programming competition contexts, this is likely Problem A from the 2017 ICPC Asia Tsukuba Regional Contest. The problem involves calculating the area of a right-angled triangle where the input consists of Pythagorean triples.

Problem Statement

Given three integers \\(a\\), \\(b\\), and \\(c\\) representing the sides of a right-angled triangle (guaranteed to be a Pythagorean triple, i.e., \\(a^2 + b^2 = c^2\\) where \\(c\\) is the hypotenuse), compute the area of the triangle. The inputs may be in any order.

Input:

Output:

Solution Approach

1. Identify the Hypotenuse: The hypotenuse is the largest side in a right-angled triangle.

2. Calculate Area: The area is half the product of the two legs (non-hypotenuse sides). Since the inputs form a Pythagorean triple, the product of the legs is always even, ensuring integer area.

Solution Code

python

import sys

def main:

data = sys.stdin.read.split

if not data:

return

index = 0

results = []

while index < len(data):

a = int(data[index])

b = int(data[index + 1])

c = int(data[index + 2])

index += 3

sides = sorted([a, b, c])

area = sides[0] * sides[1] // 2

results.append(str(area))

print('\

'.join(results))

if __name__ == "__main__":

main

Explanation

1. Reading Input: The input is read all at once for efficiency, especially given potential multiple test cases.

2. Processing Each Test Case: For every triplet of integers:

3. Output: Results for all test cases are collected and printed at once (one per line).

Example

Input:

3 4 5

5 12 13

6 8 10

Output:

30

24

This solution efficiently handles multiple test cases and leverages sorting to identify the legs of the triangle, ensuring correctness for any input order.