Q. QueryreuQ
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

A string is palindrome, if the string reads the same backward and forward. For example, strings like "a", "aa", "appa", "queryreuq" are all palindromes.

For given empty string S, you should process following two queries :

  1. Add a lower case alphabet at the back of S.
  2. Remove a character at the back of S.

After processing a query, you should count the number of palindrome substring in S. For string S and integers i,  j (1 ≤ i ≤ j ≤ |S|), represents a substring from ith to jth character of S. You should print out the number of integer pairs (i,  j) where is palindrome.

Input

Input consists of two lines.

In the first line, Q, the number of queries is given. (1 ≤ Q ≤ 10, 000)

In the second line, the query is given as string of length Q. ith character Ki denotes the ith query.

Ki is '-' or lower case alphabet ('a', 'b', ..., 'z') (without quotes).

If the character is '-', you should remove a character at the back of S. If the character is lower case alphabet, you should add a character Ki at the back of S.

It is guaranteed that length of S is always positive after the query.

Output

Print out Q space-separated integers in the first line. i-th integer should be the answer of the ith query.

Example
Input
17
qu-uer-ryr-reu-uq
Output
1 2 1 2 3 4 3 4 5 7 5 7 9 11 9 11 13