Fox and Card Game

题意翻译

桌子上有 $n$ 堆牌。每张牌上都有一个正整数。Ciel可以从任何非空牌堆的顶部取出一张牌，Jiro可以从任何非空牌堆的底部取出一张牌。Ciel先取，当所有的牌堆都变空时游戏结束。他们都想最大化他所拿牌的分数（即每张牌上正整数的和）。问他们所拿牌的分数分别是多少？

题目描述

Fox Ciel is playing a card game with her friend Fox Jiro. There are $ n $ piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game?

输入输出格式

输入格式

The first line contain an integer $ n $ ( $ 1<=n<=100 $ ). Each of the next $ n $ lines contains a description of the pile: the first integer in the line is $ s_{i} $ ( $ 1<=s_{i}<=100 $ ) — the number of cards in the $ i $ -th pile; then follow $ s_{i} $ positive integers $ c_{1} $ , $ c_{2} $ , ..., $ c_{k} $ , ..., $ c_{si} $ ( $ 1<=c_{k}<=1000 $ ) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.

输出格式

Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.

输入输出样例

输入样例 #1

2
1 100
2 1 10

输出样例 #1

101 10

输入样例 #2

1
9 2 8 6 5 9 4 7 1 3

输出样例 #2

30 15

输入样例 #3

3
3 1 3 2
3 5 4 6
2 8 7

输出样例 #3

18 18

输入样例 #4

3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000

输出样例 #4

7000 7000

说明

In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.

题意翻译

桌子上有 $n$ 堆牌。每张牌上都有一个正整数。Ciel可以从任何非空牌堆的顶部取出一张牌，Jiro可以从任何非空牌堆的底部取出一张牌。Ciel先取，当所有的牌堆都变空时游戏结束。他们都想最大化他所拿牌的分数（即每张牌上正整数的和）。问他们所拿牌的分数分别是多少？