Palindromi

You are given a sequence of $n$ characters 0 or 1, indexed by numbers $1, 2, \dots , n$. Initially every character represents a string of length one. During a concatenation two words $a$ and $b$ are chosen, deleted, and replaced by the string $ab$ such that the characters of $b$ are written after the characters of $a$.

The $n$ initial strings are concatenated to one final string using a sequence of $n-1$ concatenations. The $i$-th of those concatenation is described by a pair of indexes $(a\_i , b\_i)$, which denotes that the string containing $a\_i$-th character and the string containing $b\_i$-th character are to be concatenated. It is guaranteed that characters with indexes $a\_i$ and $b\_i$ are not in the same string.

Palindromic value of some string $w$ is defined as the total number of unique substrings of $w$ which are palindromes. We define palindromes as strings that are the same when read left to right and right to left. A substring of a string is defined as a string obtained by erasing zero or more characters from the beginning and/or ending of the string.

For every concatenation print the palindromic value of the resulting string.

The first line contains an integer $n$ ($1 ≤ n ≤ 100\\,000$), number of characters.

In the second line there is a string of $n$ characters 0 and 1 which represent the initial strings.

The $i$-th of following $n - 1$ lines contains two integers $a\_i$ and $b\_i$ ($1 ≤ a\_i , b\_i ≤ n$, $a\_i \ne b\_i$) representing the $i$-th concatenation.

Print $n - 1$ lines, the palindromic values of words obtained after each concatenation.

Clarification of the third example:

Newly created strings after every concatenation are: 00, 10, 00, 100, 1000, 001000 and 00100010. Their respective palindromic values are given in the example output. E. g. the palindromic value of 00100010 is 8 because the string contains 8 palindromic substring: 0, 00, 000, 10001, 0100010, 1, 010 and 00100.