CF204C.Little Elephant and Furik and Rubik

Little Elephant loves Furik and Rubik, who he met in a small city Kremenchug.

The Little Elephant has two strings of equal length a and b, consisting only of uppercase English letters. The Little Elephant selects a pair of substrings of equal length — the first one from string a, the second one from string b. The choice is equiprobable among all possible pairs. Let's denote the substring of a as x, and the substring of b — as y. The Little Elephant gives string x to Furik and string y — to Rubik.

Let's assume that f(x, y) is the number of such positions of i (1 ≤ i ≤ |x|), that x__i = y__i (where |x| is the length of lines x and y, and x__i, y__i are the i-th characters of strings x and y, correspondingly). Help Furik and Rubik find the expected value of f(x, y).

小象喜欢它在小城克列缅丘格结识的弗里克和鲁比克。

小象有两个等长的字符串 $a$ 和 $b$，均由大写英文字母组成。小象随机地选取一对等长的子串：第一个来自字符串 $a$，第二个来自字符串 $b$；所有可能的子串对被选中的概率均等。记从 $a$ 中选出的子串为 $x$，从 $b$ 中选出的子串为 $y$。小象将字符串 $x$ 给弗里克，将字符串 $y$ 给鲁比克。

定义 $f(x,\,y)$ 为满足 $x_i = y_i$ 的下标 $i$ 的个数（其中 $1 \le i \le |x|$；$|x|$ 表示字符串 $x$ 和 $y$ 的长度；$x_i$、$y_i$ 分别表示字符串 $x$ 和 $y$ 的第 $i$ 个字符）。请帮助弗里克和鲁比克求出 $f(x,\,y)$ 的期望值。

The first line contains a single integer n (1 ≤ n ≤ 2·105) — the length of strings a and b. The second line contains string a, the third line contains string b. The strings consist of uppercase English letters only. The length of both strings equals n.

第一行包含一个整数 $n$（$1 \leq n \leq 2 \cdot 10^5$）—— 字符串 $a$ 和 $b$ 的长度。
第二行包含字符串 $a$，第三行包含字符串 $b$。
两个字符串仅由大写英文字母组成，且长度均为 $n$。

On a single line print a real number — the answer to the problem. The answer will be considered correct if its relative or absolute error does not exceed 10 - 6.

在单行中输出一个实数——该问题的答案。只要答案的相对误差或绝对误差不超过 $10^{-6}$，即视为正确。

Let's assume that we are given string a = _a_1_a_2... a|a|, then let's denote the string's length as |a|, and its i-th character — as a__i.

A substring a[l... r] (1 ≤ l ≤ r ≤ |a|) of string a is string a__l__a__l + 1... a__r.

String a is a substring of string b, if there exists such pair of integers l and r (1 ≤ l ≤ r ≤ |b|), that b[l... r] = a.

Let's consider the first test sample. The first sample has 5 possible substring pairs: ("A", "B"), ("A", "A"), ("B", "B"), ("B", "A"), ("AB", "BA"). For the second and third pair value f(x, y) equals 1, for the rest it equals 0. The probability of choosing each pair equals , that's why the answer is · 0  +  · 1  +  · 1  +  · 0  +  · 0  =   =  0.4.

假设我们给定字符串 $a = a_1a_2\ldots a_{|a|}$，则记该字符串的长度为 $|a|$，其第 $i$ 个字符为 $a_i$。

字符串 $a$ 的子串 $a[l\ldots r]$（其中 $1 \le l \le r \le |a|$）定义为字符串 $a_la_{l+1}\ldots a_r$。

若存在整数对 $l$ 和 $r$（满足 $1 \le l \le r \le |b|$），使得 $b[l\ldots r] = a$，则称字符串 $a$ 是字符串 $b$ 的一个子串。

我们考虑第一个测试样例。该样例共有 5 种可能的子串对：("A", "B")、("A", "A")、("B", "B")、("B", "A")、("AB", "BA")。其中，第二和第三对的函数值 $f(x, y)$ 等于 1，其余各对的函数值均为 0。每一对被选中的概率均为 ，因此答案为
· 0  +  · 1  +  · 1  +  · 0  +  · 0  =   =  0.4。