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: Time Limit Exceeded)

#include <bits/stdc++.h>
#define mk make_pair
#define fs first
#define sc second
using namespace std;
typedef long long ll;
typedef long double ld;
// please, read the question correctly (do you need set or multiset)???
const int N=200010; //check the limits, dummy
int a[N];
int n, m, cnt[44];
char s[1000010];
map<string, int>mp[33];
string c[N];
int main(){
	scanf("%d",&n);
	ll ans=0;
	for(int i=0; i<n; ++i){
		scanf("%s",s);
		int sz=strlen(s);
		c[i]=s;
		string ss;
		for(int j=sz-1; j>=1; --j){
			ss+=s[j];
		}
		++mp[s[0]-'a'][ss];
	}
	set<int> st;
	for(int i=0; i<n; ++i){
		int sz=c[i].size();
		string ss;
		st.clear();
		for(int j=0; j<26; ++j)cnt[j]=0;
		for(int j=0; j<sz; ++j){
			++cnt[c[i][j]-'a'];
			st.insert(c[i][j]-'a');
		}
		for(int j=sz-1; j>=0; --j){
			for(auto it:st){
				ans+=mp[it][ss];
			}
			ss+=c[i][j];
			--cnt[c[i][j]-'a'];
			if(cnt[c[i][j]-'a']==0){
				st.erase(c[i][j]-'a');
			}
		}
	}
	ans-=n;
	cout<<ans<<endl;
}