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 1<<21
char*s,T[M],*r=T;H[M][27],h,U[M],V[M],n,k;main(i){for(;gets(r+1);++n)for(k=0;*++r&=31;)U[r-T]=k|=!!n<<*r;for(;--i+2;)for(k=0,s=r;--s>T;k=H[k][*s]=*s?H[k][*s]?:++h:0){n+=i*__builtin_popcount(U[s-T]&(V[k]|=!s[-1]<<*s));}printf("%d",1-n);}