PROBLEM STATEMENT Taro and Hanako are playing a game called Nisoku, which is played as follows. Initially, there is a pile of cards. Each card contains a real number between 1.5 and 10.0, inclusive. You are given a vector cards, the i-th element of which is the number written on the i-th card. Repeat the following step until there is only one card left in the pile: Remove any two cards from the pile, and add one new card to the pile. Write either a+b or a*b on the new card, where a and b are the numbers written on the two cards that were removed. Return the maximal possible number written on the final card in the pile. DEFINITION Class:Nisoku Method:theMax Parameters:vector Returns:double Method signature:double theMax(vector cards) NOTES -Your return value must have an absolute or relative error less than 1e-9. CONSTRAINTS -cards will contain between 2 and 50 elements, inclusive. -Each element of cards will be between 1.5 and 10.0, inclusive. EXAMPLES 0) {5, 8} Returns: 40.0 5 * 8 = 40. 1) {1.5, 1.8} Returns: 3.3 1.5 + 1.8 = 3.3. 2) {8.26, 7.54, 3.2567} Returns: 202.82857868 3) {1.5, 1.7, 1.6, 1.5} Returns: 9.920000000000002 4) {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10} Returns: 1.0E50 The answer can be extremely big. This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2010, TopCoder, Inc. All rights reserved.