Suffix Subgroup
Description
You are given a group of n strings: s1, s2, ..., sn.
You should find a subgroup si1, si2, ..., sik (1 ≤ i1 < i2 < ... < ik ≤ n) of the group. The following two conditions must hold:
- there exists a string t such, that each string from found subgroup is its suffix;
- the number of strings in the found subgroup is as large as possible.
Your task is to print the number of strings in the found subgroup.
The first line contains an integer n (1 ≤ n ≤ 105) — the number of strings in the group. Each of the next n lines contains a string. The i-th line contains non-empty string si.
Each string consists only from lowercase Latin letters. The sum of all strings si doesn't exceed 105.
Output a single integer — the number of strings in the found subgroup.
Input
The first line contains an integer n (1 ≤ n ≤ 105) — the number of strings in the group. Each of the next n lines contains a string. The i-th line contains non-empty string si.
Each string consists only from lowercase Latin letters. The sum of all strings si doesn't exceed 105.
Output
Output a single integer — the number of strings in the found subgroup.
Samples
6
bb
bb
b
aaa
aa
z
3
Note
Look at the test sample. The required subgroup is s1, s2, s3.