Codeforces Fox and Card Game (greedy, sort)

C. Fox and Card Gametime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output

Fox Ciel is playing a card game with her friend Fox Jiro. There is n piles of cards on the table. And there is a positive an 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 integerN(1≤N≤100). Each of the nextNLines contains a description of the pile:the first integer in the s i (1≤ s i ≤100)-the number of cards in The  i -th pile; then fo Llow  s i  positive integers < Span class= "Tex-span" > C 1,  C 2, ...,   C K , ...,   C s i   ( Span class= "Tex-span" >1≤ C k ≤1000)-the sequence of the numbers on the card s listed from top of the pile to bottom of the pile.

Output

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

Sample Test (s) input

2
1 100
2 1 10

Output

101 10

Input

1
9 2 8 6 5 9 4 7 1 3

Output

30 15

Input

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

Output

18 18

Input

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

Output

7000 7000

Note

In the first example, Ciel'll take the cards with number and 1, Jiro'll take the card with Number 10.

In the second example, Ciel'll take cards with numbers 2, 8, 6, 5, 9 and Jiro would take cards with numbers 4, 7, 1, 3.

The title means there are n stacks of cards, each pile of cards have Si Zhang Card, each card has a weight, a can only from the above card, B can only take the card from below, two people have taken the best strategy, ask the last two people to take the weight of the total number of cards.

Can analyze, if

Codeforces Fox and Card Game (greedy, sort)