Dima adds letters s₁, …, 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?

The input contains a string s₁ … s_n consisting of letters ‘a’ and ‘b’ (1 ≤ n ≤ 5 000 000).

Print n numbers without spaces: i-th number must be the number of palindrome substrings of the prefix s₁ … s_i minus the number of palindrome substrings of the prefix s₁ … s_i−1. The first number in the output should be one.

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).