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D. String

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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*.

Input

The only line contains the given string *s*, consisting only of small Latin letters (1 ≤ |*s*| ≤ 10^{5}).

Output

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.

Examples

Input

aaaa

Output

20

Input

abcdef

Output

21

Input

abacabadabacaba

Output

188

Note

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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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