F. Smallertime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAlperen has two strings, s and t which are both initially equal to "a". He will perform q operations of two types on the given strings:  1 \;\; k \;\; x — Append the string x exactly k times at the end of string s. In other words, s := s + \underbrace{x + \dots + x}_{k \text{ times}}.  2 \;\; k \;\; x — Append the string x exactly k times at the end of string t. In other words, t := t + \underbrace{x + \dots + x}_{k \text{ times}}. After each operation, determine if it is possible to rearrange the characters of s and t such that s is lexicographically smaller^{\dagger} than t.Note that the strings change after performing each operation and don't go back to their initial states.^{\dagger} Simply speaking, the lexicographical order is the order in which words are listed in a dictionary. A formal definition is as follows: string p is lexicographically smaller than string q if there exists a position i such that p_i < q_i, and for all j < i, p_j = q_j. If no such i exists, then p is lexicographically smaller than q if the length of p is less than the length of q. For example, \texttt{abdc} < \texttt{abe} and \texttt{abc} < \texttt{abcd}, where we write p < q if p is lexicographically smaller than q.InputThe first line of the input contains an integer t (1 \leq t \leq 10^4) — the number of test cases.The first line of each test case contains an integer q (1 \leq q \leq 10^5) — the number of operations Alperen will perform.Then q lines follow, each containing two positive integers d and k (1 \leq d \leq 2; 1 \leq k \leq 10^5) and a non-empty string x consisting of lowercase English letters — the type of the operation, the number of times we will append string x and the string we need to append respectively.It is guaranteed that the sum of q over all test cases doesn't exceed 10^5 and that the sum of lengths of all strings x in the input doesn't exceed 5 \cdot 10^5.OutputFor each operation, output "YES", if it is possible to arrange the elements in both strings in such a way that s is lexicographically smaller than t and "NO" otherwise.ExampleInput
352 1 aa1 2 a2 3 a1 2 b2 3 abca21 5 mihai2 2 buiucani31 5 b2 3 a2 4 paiuOutput
YES
NO
YES
NO
YES
NO
YES
NO
NO
YES
NoteIn the first test case, the strings are initially s =  "a" and t =  "a". After the first operation the string t becomes "aaa". Since "a" is already lexicographically smaller than "aaa", the answer for this operation should be "YES".After the second operation string s becomes "aaa", and since t is also equal to "aaa", we can't arrange s in any way such that it is lexicographically smaller than t, so the answer is "NO".After the third operation string t becomes "aaaaaa" and s is already lexicographically smaller than it so the answer is "YES".After the fourth operation s becomes "aaabb" and there is no way to make it lexicographically smaller than "aaaaaa" so the answer is "NO".After the fifth operation the string t becomes "aaaaaaabcaabcaabca", and we can rearrange the strings to: "bbaaa" and "caaaaaabcaabcaabaa" so that s is lexicographically smaller than t, so we should answer "YES". 
352 1 aa1 2 a2 3 a1 2 b2 3 abca21 5 mihai2 2 buiucani31 5 b2 3 a2 4 paiu
YES NO YES NO YES NO YES NO NO YES 
['constructive algorithms', 'greedy', 'strings', '*1500']