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).
输入描述:
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.
输出描述:
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.
备注:
Let's assume that we are given string a = a1a2... aa, then let's denote the string's length as a, and its i-th character — as ai.A substring a[l... r](1 ≤ l ≤ r ≤ a) of string a is string alal + 1... ar.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.
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