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E. Mike and Friends

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWhat-The-Fatherland is a strange country! All phone numbers there are strings consisting of lowercase English letters. What is double strange that a phone number can be associated with several bears!

In that country there is a rock band called CF consisting of *n* bears (including Mike) numbered from 1 to *n*.

Phone number of *i*-th member of CF is *s*_{i}. May 17th is a holiday named Phone Calls day. In the last Phone Calls day, everyone called all the numbers that are substrings of his/her number (one may call some number several times). In particular, everyone called himself (that was really strange country).

Denote as *call*(*i*, *j*) the number of times that *i*-th member of CF called the *j*-th member of CF.

The geek Mike has *q* questions that he wants to ask you. In each question he gives you numbers *l*, *r* and *k* and you should tell him the number

Input

The first line of input contains integers *n* and *q* (1 ≤ *n* ≤ 2 × 10^{5} and 1 ≤ *q* ≤ 5 × 10^{5}).

The next *n* lines contain the phone numbers, *i*-th line contains a string *s*_{i} consisting of lowercase English letters ().

The next *q* lines contain the information about the questions, each of them contains integers *l*, *r* and *k* (1 ≤ *l* ≤ *r* ≤ *n* and 1 ≤ *k* ≤ *n*).

Output

Print the answer for each question in a separate line.

Examples

Input

5 5

a

ab

abab

ababab

b

1 5 1

3 5 1

1 5 2

1 5 3

1 4 5

Output

7

5

6

3

6

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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