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"
#include <boost/multi_array.hpp>
#include <boost/optional.hpp>
#include <boost/range/irange.hpp>
#include <boost/range/algorithm.hpp>
#include <boost/range/adaptors.hpp>
#include <boost/dynamic_bitset.hpp>
namespace adaptor = boost::adaptors;
using index_t = std::size_t;

namespace lib
{
	using graph_t = std::vector<std::set<index_t>>;
	template<class T>using weighted_graph_t = std::vector<std::map<index_t, T>>;

	struct max_t
	{
		template<class T>constexpr T operator()(T const& lhs, T const& rhs)const
		{
			return std::max(lhs, rhs);
		}
	};
	struct min_t
	{
		template<class T>constexpr T operator()(T const& lhs, T const& rhs)const
		{
			return std::min(lhs, rhs);
		}
	};

	constexpr max_t max;
	constexpr min_t min;

	template<class T>auto order_by(T func)
	{
		return [=](auto&& lhs, auto&& rhs)
		{
			return func(lhs) < func(rhs);
		};
	}

	template<class T>constexpr auto max_v = std::numeric_limits<T>::max();
	template<class T>constexpr auto min_v = std::numeric_limits<T>::min();

	template<class T>using p_queue = std::priority_queue<T, std::vector<T>, std::greater<>>;
}

void Main()
{
	constexpr std::size_t X = 26;
	int N;
	std::cin >> N;
	std::vector<std::string> vec(N);
	std::map<std::string_view, std::array<std::int64_t, X>> map;
	for (auto& str : vec)
	{
		std::cin >> str;
		std::string_view view = str;
		for (auto i : boost::irange(str.size()))
		{
			view.remove_prefix(1);
			std::array<bool, X> flag{};
			for (auto k : boost::irange(i + 1))
			{
				flag[str[k] - 'a'] = true;
			}
			for (auto i : boost::irange(X))
			{
				map[view][i] += flag[i];
			}
		}
	}
	std::int64_t count = 0;
	for (auto&& str : vec)
	{
		std::string_view view = str;
		view.remove_prefix(1);
		count += map[view][str[0] - 'a'] - 1;
	}
	std::cout << count << std::endl;
}

int main()
{
	std::cin.tie(nullptr);
	std::ios_base::sync_with_stdio(false);
	std::cout << std::fixed << std::setprecision(15);
	Main();
}