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 defaultdict
def h():
    return [0] * 26

def main():
    N = int(input())
    M = defaultdict(h)
    S = []
    for _ in range(N):
        s = memoryview(bytes(input()[::-1], 'utf-8'))
        S.append(s)
        hs = set()
        for i in reversed(range(len(s))):
            head = s[i] - 97
            hs.add(head)
            for j in hs:
                M[s[:i]][j] += 1
    r = 0
    for s in S:
        r += M[s[:-1]][s[-1] - 97] - 1
    return r

print(main())