Problem:
Score : 700 points

Problem Statement

Limak can repeatedly remove one of the first two characters of a string,
for example abcxyx \rightarrow acxyx \rightarrow cxyx \rightarrow cyx.

You are given N different strings S_1, S_2, \ldots, S_N.
Among N \cdot (N-1) / 2 pairs (S_i, S_j),
in how many pairs could Limak obtain one string from the other?

Constraints

2 \leq N \leq 200\,000

S_i consists of lowercase English letters a-z.

S_i \neq S_j

1 \leq |S_i|

|S_1| + |S_2| + \ldots + |S_N| \leq 10^6

Input

Input is given from Standard Input in the following format.

N
S_1
S_2
\vdots
S_N

Output

Print the number of unordered pairs (S_i, S_j)
where i \neq j and Limak can obtain one string from the other.

Sample Input 1

3
abcxyx
cyx
abc

Sample Output 1

1

The only good pair is (abcxyx, cyx).

Sample Input 2

6
b
a
abc
c
d
ab

Sample Output 2

5

There are five good pairs: (b, abc), (a, abc), (abc, c), (b, ab), (a, ab).

Solution in Python (3.8.2) (judge verdict: Time Limit Exceeded)

from collections import defaultdict

n = int(input())

ss = [input() for _ in range(n)]

ss.sort(key=len)

ans = 0
m0 = set()
m = defaultdict(lambda: set())
ml = {}
ls = set()

for s in ss:
    ans += len(m0 & set(s))
    s1 = s[1:]
    l = len(s1)
    if l == 0:
        m0.add(s)
        continue

    si = set(s[-i:] for i in ls)
    for k in m.keys() & si:
        ans += len(m[k] & set(s[:-ml[k]]))

    m[s1].add(s[0])
    ml[s1] = l
    ls.add(l)

print(ans)