10335 - 游戏

有如下一个双人游戏:N(2 <= N <= 100)个正整数的序列放在一个游戏平台上，两人轮流从序列的两端取数，取数后该数字被去掉并累加到本玩家的得分中，当数取尽时，游戏结束。以最终得分多者为胜。

编一个执行最优策略的程序，最优策略就是使自己能得到在当前情况下最大的可能的总分的策略。你的程序要始终为第二位玩家执行最优策略。

第一行: 正整数N, 表示序列中正整数的个数。
第二行至末尾: 用空格分隔的N个正整数（大小为1-200）。

只有一行，用空格分隔的两个整数: 依次为玩家一和玩家二最终的得分。

A Game IOI'96 - Day 1 Consider the following two-player game played with a sequence of N positive integers (2 <= N <= 100) laid onto a game board. Player 1 starts the game. The players move alternately by selecting a number from either the left or the right end of the sequence. That number is then deleted from the board, and its value is added to the score of the player who selected it. A player wins if his sum is greater than his opponents.

Write a program that implements the optimal strategy. The optimal strategy yields maximum points when playing against the "best possible" opponent. Your program must further implement an optimal strategy for player 2.

PROGRAM NAME: game1 INPUT FORMAT Line 1: N, the size of the board
Line 2-etc: N integers in the range (1..200) that are the contents of the game board, from left to right

SAMPLE INPUT (file game1.in) 6 4 7 2 9 5 2

OUTPUT FORMAT Two space-separated integers on a line: the score of Player 1 followed by the score of Player 2. SAMPLE OUTPUT (file game1.out) 18 11