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 C (GCC 9.2.1) (judge verdict: Accepted)

#define M'   '
char*s,T[M],*r=T;U[M*35];n;k;main(i){for(;gets(r+1);k=!--n)for(;*++r&=31;)U[r-T]=k|=!!n<<*r;for(;~i--;)for(s=r;s-->T;k=U[k]=U[k-=~-~*s*M]?:*s?s-T:0)n+=__builtin_popcount(U[s-T]&(U[k+M]^=!s[-1]<<*s));printf("%d\n",n+1);}