C. Fox and Card Game
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
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?
Input
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 si(1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel‘s cards and the sum of Jiro‘s cards if they play optimally.
Sample test(s)
input
21 1002 1 10
output
101 10
input
19 2 8 6 5 9 4 7 1 3
output
30 15
input
33 1 3 23 5 4 62 8 7
output
18 18
input
33 1000 1000 10006 1000 1000 1000 1000 1000 10005 1000 1000 1000 1000 1000
output
7000 7000
Note
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.
题目的意思是有n堆牌，每一堆牌有si张牌，每张牌都有一个权值，A只能从上面拿牌，B只能从下面拿牌，两个人都采取最优的策略，问最后两个人拿的牌的权值总和是多少。
可以分析一下，如果