Two strings u₁ u₂ ... u_k and v₁ v₂ ... v_l are isomorphic if and only if k = l and there exists a injection g such that u_i = g(v_i) for all i ∈ {1, 2, ..., k}.
Note that a function f is injection if and only if f(x) ≠ f(y) for all x ≠ y.
Bobo would like to choose some strings from all n(n +1)/2 substrings of the given string s₁ s₂ ... s_n.
Find out the maximum number of strings he may choose so that no two chosen strings are isomorphic.

The input consists of several test cases and is terminated by end-of-file.
The first line of each test case contains an integer n.
The second line contains a string s1, s2, ..., sn.

For each test case, print an integer which denotes the result.

4
abaa
4
abab

6
4

* 1 ≤ n ≤ 5x 104
* si ∈ {a, b, c}
* The sum of n does not exceed 2 x 105.