Unique Prefix Character Check

You are given a string s consisting of lowercase English letters and a list of integers p of length equal to the length of s. The list p specifies the required number of unique characters for each prefix of s. In other words, for every i from 1 to |s|, the substring s[0:i] must contain exactly p[i-1] distinct characters.

Your task is to determine whether the string s satisfies these conditions. Formally, let \( s = s_1 s_2 \cdots s_n \) and let \( p = [p_1, p_2, \dots, p_n] \). The condition that must be met is:

[ \forall, 1 \le i \le n,\quad |{ s_1, s_2, \dots, s_i }| = p_i ]

If the condition holds for all prefixes, print True. Otherwise, print False.

inputFormat

The input is given on standard input and consists of two lines:

• The first line contains the string s.
• The second line contains \( n \) space-separated integers which represent the list p (where \( n \) is the length of s). In the case that s is empty, the second line will also be empty.

outputFormat

Print a single line True if for every prefix of s the number of unique characters equals the corresponding value in p, and False otherwise.

abac
1 2 2 3

True