문제

There are a total of $N$ ($1\le N\le 5000$) cows on the number line, each of which is a Holstein or a Guernsey. The breed of the $i$-th cow is given by $b_i\in \{H,G\}$, the location of the $i$-th cow is given by $x_i$ ($0 \leq x_i \leq 10^9$), and the weight of the $i$-th cow is given by $y_i$ ($1 \leq y_i \leq 10^5$).

At Farmer John's signal, some of the cows will form pairs such that

Every pair consists of a Holstein $h$ and a Guernsey $g$ whose locations are within $K$ of each other ($1\le K\le 10^9$); that is, $|x_h-x_g|\le K$.Every cow is either part of a single pair or not part of a pair.The pairing is maximal; that is, no two unpaired cows can form a pair.

It's up to you to determine the range of possible sums of weights of the unpaired cows. Specifically,

If $T=1$, compute the minimum possible sum of weights of the unpaired cows.If $T=2$, compute the maximum possible sum of weights of the unpaired cows.

입력

The first input line contains $T$, $N$, and $K$.

Following this are $N$ lines, the $i$-th of which contains $b_i,x_i,y_i$. It is guaranteed that $0\le x_1< x_2< \cdots< x_N\le 10^9$.

출력

The minimum or maximum possible sum of weights of the unpaired cows.

예제 입력 1

2 5 4
G 1 1
H 3 4
G 4 2
H 6 6
H 8 9

예제 출력 1

16

예제 입력 2

1 5 4
G 1 1
H 3 4
G 4 2
H 6 6
H 8 9

예제 출력 2

6

예제 입력 3

2 10 76
H 1 18
H 18 465
H 25 278
H 30 291
H 36 202
G 45 96
G 60 375
G 93 941
G 96 870
G 98 540

예제 출력 3

1893

점수

Test cases 4-7 satisfy $T=1$.Test cases 8-14 satisfy $T=2$ and $N\le 300$.Test cases 15-22 satisfy $T=2$.

Note: the memory limit for this problem is 512MB, twice the default.