13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T663,

You are given $$$n$$$ strings $$$s_1, s_2, \dots, s_n$$$, consisting of lowercase Latin letters. Let $$$|x|$$$ be the length of string $$$x$$$.

Let a collapse $$$C(a, b)$$$ of two strings $$$a$$$ and $$$b$$$ be the following operation:

if $$$a$$$ is empty, $$$C(a, b) = b$$$;
if $$$b$$$ is empty, $$$C(a, b) = a$$$;
if the last letter of $$$a$$$ is equal to the first letter of $$$b$$$, then $$$C(a, b) = C(a_{1,|a|-1}, b_{2,|b|})$$$, where $$$s_{l,r}$$$ is the substring of $$$s$$$ from the $$$l$$$-th letter to the $$$r$$$-th one;
otherwise, $$$C(a, b) = a + b$$$, i. e. the concatenation of two strings.

Calculate $$$\sum\limits_{i=1}^n \sum\limits_{j=1}^n |C(s_i, s_j)|$$$.

Input

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^6$$$).

Each of the next $$$n$$$ lines contains a string $$$s_i$$$ ($$$1 \le |s_i| \le 10^6$$$), consisting of lowercase Latin letters.

Collapsing Strings

Examples