What-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

The next n lines contain the phone numbers, i-th line contains a string s_iconsisting 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

5 5
a
ab
abab
ababab
b
1 5 1
3 5 1
1 5 2
1 5 3
1 4 5

7
5
6
3
6

題意：給定N個串，M次詢問，每次詢問[L,R]裏含多少個X。

思路：（第一次做，結合主席樹那裏還是不太好想）。對N個串建立AC自動機，建立Fail樹，然後得到DFS序。那麽，對於每個串S，假設其長度為L，S在AC自動機上面跑，其每個前綴Si在AC自動機上面得到最大深度，對應的Fail樹位置，貢獻加1，保證這個貢獻在Si的後綴的子樹裏（比如abcdef，那麽跑到abcd時，在fail樹上面對應的位置貢獻加1 ，對於後綴abcd,bcd,cd,d的子樹都含這個貢獻）。

關鍵是如何出現子樹來自於[L,R]的貢獻。開始我以為以dfs序為X軸，以來自的串為Y軸建立主席樹，查詢的時候查詢區間[in[u],out[u]]，即子樹裏關鍵字在[L,R]裏的個數。但是發現沒有轉移關系。所以想不走了。

看了其他人的代碼，是以每個串，以來自的串為X軸（從長的前綴到短的前綴），以dfs序為X軸，保證了前綴和的正確性，查詢的時候查詢區間[L-1,R]的區間在[in[[u],out[u]]的數量。

CodeForces 547E：Mike and Friends（AC自動機+DFS序+主席樹）