Hidden Codes

A set of code words and a text are given. The text is supposed to contain a message made up of the code words embedded in the text in a peculiar (and possibly ambiguous) way.

The code words and the text are sequences made up of the upper and lower case letters of the English alphabet only. Case-sensitivity is assumed. The length of a code word is defined in the usual way: For example, the code word ALL has length 3.

The letters of a code word do not have to occur consecutively in the given text. For example, the code word ALL will always occur in the text within a subsequence in the form of AuLvL where u and v denote arbitrary (possibly empty) sequences of letters. We say that AuLvL is a covering sequence for ALL. In general, a covering sequence for a code word is defined as a substring of the text such that the first letter and the last letter of the substring are the same as those of the code word and it is possible to obtain the code word by deleting some (possibly none) of the letters of the substring. It should be noted that a code word may occur within one or more covering sequences or may not occur in the text at all, and that a covering sequence may be a covering sequence for more than one code word.

A covering sequence is identified by its start position (position of its first letter) and its end position (position of its last letter) in the text. (The first letter of the text is at position 1.) We say that two covering sequences, say c1 and c2, do not overlap if the start position of c1 is greater than (>) the end position of c2 or vice versa. Otherwise we say that the two covering sequences overlap.

To extract the message hidden in the text you undertake the task of forming a solution. A solution is a set of items, each consisting of a code word and a covering sequence for this code word, so that the following conditions are all satisfied:

1. the covering sequences do not overlap with each other;
2. a covering sequence does not exceed 1000 in length;
3. the sum of the lengths of the code words is maximal. (Each item contributes the length of the code word it contains to the sum.)

In case there is more than one solution you are required to report only one solution.

Input

The first line of input contains the number of code words, N (1 ≤ N ≤ 100). Each of the following N lines contains one code word. Each code word has a numerical ID. IDs are assigned in increasing order starting from 1 (hence the first code word has the ID 1, the second 2, and so on). No code word has a length greater than 100.
The final line of input is the text, whose length is at least 1 character and no more than 1 000 000 characters.

We say that a covering sequence c for a code word w is right-minimal if no proper prefix of c (a proper prefix is an initial subsequence of c that is not equal to c) is a covering sequence for w. For example, for the code word ALL, AAALAL is a right-minimal covering sequence whereas AAALALAL is also a covering sequence, but not right-minimal.

It is guaranteed that in the given text:

1. for each position in the text the number of right-minimal covering sequences containing that position does not exceed 2500;
2. the number of right-minimal covering sequences does not exceed 10 000.

Output

The first line of output should contain the sum obtained by your solution. Each of the following lines will determine an item in your solution. A line consists of three space-separated integers: i, s, and e. Here i is the ID-number of the code word that occurs within the covering sequence identified by the start position s and end position e. The order of the output lines that follow the first line is not important.

Sample Input

```4
RuN
RaBbit
HoBbit
StoP
StXRuYNvRuHoaBbvizXztNwRRuuNNP
```

Sample Output

```12
2 9 21
1 4 7
1 24 28
```

(Remark: The hidden message that could be extracted from the solution is "RuN RaBbit RuN". (An alternative solution would yield "RuN HoBbit RuN"). Be reminded that the message is not to appear in the output.)

Point Value: 20 (partial)
Time Limit: 2.00s
Memory Limit: 16M

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

• (0/0)
this only seems to accept ONE solution, and not ALL valid solutions.
Solutions with the maximum score are accepted only some of the time, even when they seem to be valid (many assertions such as length < 1000, it is confirmed to contain a right-minimal sequence, etc. )
For example, changing a check in code from
> maximum score so far to >= maximum score so far
would change the amount of test cases that are correct, even though maximum score(message length) remains the same

• (0/0)
Yeah, you're right, I never got around to implementing the judge for this one.
I'll rejudge your solution after I do.

• (0/0)
Fixed!

• (0/0)
Um, my code is outputting the correct sum, but 4/10 times my solution is judged as incorrect ... (7 years later!)

• (1/0)
I'll take a look.

Edit: I have manually verified that your solution is incorrect, although your sum is correct.