A10738 | Hongcow Buys a Deck of Cards

One day, Hongcow goes to the store and sees a brand new deck of $n$ special cards. Each individual card is either red or blue. He decides he wants to buy them immediately. To do this, he needs to play a game with the owner of the store.

This game takes some number of turns to complete. On a turn, Hongcow may do one of two things:

- Collect tokens. Hongcow collects $1$ red token and $1$ blue token by choosing this option (thus, $2$ tokens in total per one operation).
- Buy a card. Hongcow chooses some card and spends tokens to purchase it as specified below.

The $i$ -th card requires $r_{i}$ red resources and $b_{i}$ blue resources. Suppose Hongcow currently has $A$ red cards and $B$ blue cards. Then, the $i$ -th card will require Hongcow to spend $max(r_{i}-A,0)$ red tokens, and $max(b_{i}-B,0)$ blue tokens. Note, only tokens disappear, but the cards stay with Hongcow forever. Each card can be bought only once.

Given a description of the cards and their costs determine the minimum number of turns Hongcow needs to purchase all cards.

The first line of input will contain a single integer $n$ ( $1<=n<=16$ ).

The next $n$ lines of input will contain three tokens $c_{i}$ , $r_{i}$ and $b_{i}$ . $c_{i}$ will be 'R' or 'B', denoting the color of the card as red or blue. $r_{i}$ will be an integer denoting the amount of red resources required to obtain the card, and $b_{i}$ will be an integer denoting the amount of blue resources required to obtain the card ( $0<=r_{i},b_{i}<=10^{7}$ ).

Output a single integer, denoting the minimum number of turns needed to acquire all the cards.