Dima adds letters *s*_{1}, …, *s*_{n} one by one to the end of a word. After each letter, he asks Misha to tell him how many new palindrome substrings appeared
when he added that letter.
Two substrings are considered distinct if they are different as strings.
Which *n* numbers will be said by Misha if it is known that he is never wrong?

### Input

The input contains a string *s*_{1} … *s*_{n} consisting of letters ‘a’ and ‘b’ (1 ≤ *n* ≤ 5 000 000).

### Output

Print *n* numbers without spaces: *i*-th number must be the number of palindrome substrings of the prefix *s*_{1} … *s*_{i} minus the number of palindrome
substrings of the prefix *s*_{1} … *s*_{i−1}.
The first number in the output should be one.

### Sample

### Notes

We guarantee that jury has C++ solution which fits Time Limit at least two times. We do not guarantee that solution on other languages exists (even Java).

**Problem Author: **Mikhail Rubinchik (prepared by Kirill Borozdin)

**Problem Source: **Ural FU Dandelion contest. Petrozavodsk training camp. Summer 2014