You are given a string s. Each pair of numbers l and r that fulfill the condition 1 ≤ l ≤ r ≤ |s|, correspond to a substring of the string s, starting in the position l and ending in the position r (inclusive).
Let's define the function of two strings F(x, y) like this. We'll find a list of such pairs of numbers for which the corresponding substrings of string x are equal to string y. Let's sort this list of pairs according to the pair's first number's increasing. The value of function F(x, y) equals the number of non-empty continuous sequences in the list.
For example: F(babbabbababbab, babb) = 6. The list of pairs is as follows:
(1, 4), (4, 7), (9, 12)
Its continuous sequences are:
Your task is to calculate for the given string s the sum F(s, x) for all x, that x belongs to the set of all substrings of a string s.
The only line contains the given string s, consisting only of small Latin letters (1 ≤ |s| ≤ 105).
Print the single number — the sought sum.
Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.
In the first sample the function values at x equal to "a", "aa", "aaa" and "aaaa" equal 10, 6, 3 and 1 correspondingly.
In the second sample for any satisfying x the function value is 1.