You are given a string s. Each pair of numbers l and r that fulfill the condition 1 \le l \le r \le |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:
(1,4) (4,7) (9,12) (1,4),(4,7) (4,7),(9,12) (1,4),(4,7),(9,12)
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 \le |s| \le 105).

Print the single number - the sought sum.

Please do not use the %lld specificator to read or write 64-bit integers in C++. 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.