C. Hongcow Buys a Deck of Cards
time limit per test
2 seconds
memory limit per test
256 megabytes
standard input
standard output

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 ≤ 107).


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

R 0 1
B 1 0
R 1 1
R 3 0
R 2 0
R 1 0

For the first sample, Hongcow's four moves are as follows:

  1. Collect tokens
  2. Buy card 1
  3. Buy card 2
  4. Buy card 3
Note, at the fourth step, Hongcow is able to buy card 3 because Hongcow already has one red and one blue card, so we don't need to collect tokens.

For the second sample, one optimal strategy is as follows:

  1. Collect tokens
  2. Collect tokens
  3. Buy card 2
  4. Collect tokens
  5. Buy card 3
  6. Buy card 1
At the fifth step, even though Hongcow has a red token, Hongcow doesn't actually need to spend it, since Hongcow has a red card already.