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Time Limit: 2 s Memory Limit: 512 MB Total points: 100
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# 2152. Paired Up

Statistics

There are a total of N (1N5000) cows on the number line, each of which is a Holstein or a Guernsey. The breed of the i-th cow is given by biH,G, the location of the i-th cow is given by xi (0xi109), and the weight of the i-th cow is given by yi (1yi105).

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 (1K109); that is, |xhxg|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.

Input Format

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

Following this are N lines, the i-th of which contains bi,xi,yi. It is guaranteed that 0x1<x2<<xN109.

Output

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

Examples

Input 1

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

Output 1

16

Cows 2 and 3 can pair up because they are at distance 1, which is at most K=4. This pairing is maximal, because cow 1, the only remaining Guernsey, is at distance 5 from cow 4 and distance 7 from cow 5, which are more than K=4. The sum of weights of unpaired cows is 1+6+9=16.

Input 2

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

Output 2

6

Cows 1 and 2 can pair up because they are at distance 2K=4, and cows 3 and 5 can pair up because they are at distance 4K=4. This pairing is maximal because only cow 4 remains. The sum of weights of unpaired cows is the weight of the only unpaired cow, which is simply 6.

Input 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

Output 3

1893

The answer to this example is 18+465+870+540=1893.

Scoring

  • Test cases 4-7 satisfy T=1.
  • Test cases 8-14 satisfy T=2 and N300.
  • Test cases 15-22 satisfy T=2.

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

Problem credits: Benjamin Qi