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: Wrong Answer)

from random import randint
mod=1370757747362922367
rr=randint(2,mod-2)
n=int(input())
ss=[(input()+"{")[::-1]for _ in range(n)]
ss.sort(key=len)
d={}
ans=0
for s in ss:
  x=ord(s[-1])-ord("a")
  r=1
  h=0
  y=[0]*27
  for t in s:y[ord(t)-ord("a")]+=1
  for t in s[:-1]:
    y[ord(t)-ord("a")]-=1
    h=(h+(ord(t)-ord("a"))*r)%mod
    r=(r*rr)%mod
    if h in d:
      for i in range(27):
        if y[i]:ans+=d[h][i]
  if h not in d:d[h]=[0]*27
  d[h][x]+=1
print(ans)