codeforces 1607D.Blue-Red Permutation_codeforce 1607 d

D. Blue-Red Permutation

You are given an array of integers a of length n. The elements of the
array can be either different or the same.

Each element of the array is colored either blue or red. There are no
unpainted elements in the array. One of the two operations described
below can be applied to an array in a single step:

either you can select any blue element and decrease its value by 1; or
you can select any red element and increase its value by 1. Situations
in which there are no elements of some color at all are also possible.
For example, if the whole array is colored blue or red, one of the
operations becomes unavailable.

Determine whether it is possible to make 0 or more steps such that the
resulting array is a permutation of numbers from 1 to n?

In other words, check whether there exists a sequence of steps
(possibly empty) such that after applying it, the array a contains in
some order all numbers from 1 to n (inclusive), each exactly once.

Input The first line contains an integer t (1≤t≤104) — the number of
input data sets in the test.

The description of each set of input data consists of three lines. The
first line contains an integer n (1≤n≤2⋅105) — the length of the
original array a. The second line contains n integers a1, a2, …, an
(−109≤ai≤109) — the array elements themselves.

The third line has length n and consists exclusively of the letters
‘B’ and/or ‘R’: ith character is ‘B’ if ai is colored blue, and is ‘R’
if colored red.

It is guaranteed that the sum of n over all input sets does not exceed
2⋅105.

Output Print