A8336. String

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:

- $(1,4)$
- $(4,7)$
- $(9,12)$
- $(1,4),(4,7)$
- $(4,7),(9,12)$
- $(1,4),(4,7),(9,12)$

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 ( $1<=|s|<=10^{5}$ ).

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.