Birthday Memorization

Krarkl wants to learn the birthdays of all his $N$ friends, so he knows whom to congratulate each day. Unfortunately collisions sometimes arise, meaning several friends may have the same birthday. This may confuse Krarkl, so he decided to only remember the birthday of the friend he likes the most in case of a collision. Given a list of birthdays for each of his friends and how much Krarkl likes each friend, print what friends Krarkl will remember the birthday for.

The first line of input contains an integer $N$ ($1 \leq N \leq 2\, 000$), the number of friends.

Then $N$ lines follow,
one for each friend. The $i$’th of these lines contains a
string with the $i$’th
friend’s first name $S_ i$
($S_ i$ will be between
$1$ and $10$ letters long), an integer
$C_ i$ ($0 \leq C_ i \leq 100\, 000$) denoting
how much Krarkl likes the friend, and their birthday given in
the format `DD/MM` (where `DD` is a day between `01` and `31`, and
`MM` is a month between `01` and `12`). A higher
value of $C_ i$ means that
Krarkl likes that friend more.

The birthdays will be real dates during 2020 (a leap year),
for example `28/02` for February 28.
All names will consist only of small English letters
(`a-z`) with a capital first letter
(`A-Z`). All $C_ i$ will be distinct.

On the first line, print an integer $K$ – the number of friends whose birthdays Krarkl will remember.

This should be followed by $K$ lines containing a single word
each, the first names of the chosen friends, **in lexicographical order**.

Your solution will be tested on a number of test case groups. To get the points for a group, you need to pass all test cases in the group.

Group |
Points |
Constraints |

$1$ |
$30$ |
$N \leq 100$ |

$2$ |
$70$ |
No further constraints |

In the first sample, Sanna and Simon have the same birthday. Since Krarkl likes Sanna less than Simon ($1 < 2$), Krarkl will only remember Simon’s and Saga’s birthdays.

In the second sample, Krarkl has really bad luck and will miss half of his friends’ birthdays.

Sample Input 1 | Sample Output 1 |
---|---|

3 Sanna 1 16/03 Simon 2 16/03 Saga 3 14/10 |
2 Saga Simon |

Sample Input 2 | Sample Output 2 |
---|---|

10 Oden 78 03/12 Tor 132 14/05 Freja 10000 14/05 Loke 512 12/10 Hel 14 04/05 Fjorgynn 532 13/05 Hildegun 500 13/05 Vindsval 17 03/12 Snotra 20 04/05 Kvaser 420 03/12 |
5 Fjorgynn Freja Kvaser Loke Snotra |