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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

from collections import Counter

n = int(input())
sss = [input() for _ in range(n)]
d = {s[1:]: 0 for s in sss}

for s in sss:
    cnt = Counter(s)
    flag = 0
    for c in cnt:
        k = ord(c) - 97
        flag |= 1 << (k * 20)
    if '' in d:
        d[''] += flag
    for i in range(len(s) - 1, 0, -1):
        c = s[i]
        cnt[c] -= 1
        if cnt[c] == 0:
            flag ^= 1 << ((ord(c) - 97) * 20)
        if s[i:] in d:
            d[s[i:]] += flag

ans = 0
mask = (1 << 20) - 1
for s in sss:
    flag = d[s[1:]]
    bs = ((ord(s[0]) - 97) * 20)
    cnt = (flag >> bs) & mask
    ans += cnt - 1

print(ans)