E. Double Permutation Inc.time limit per test5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputPolycarp recently became an employee of the company "Double Permutation Inc." Now he is a fan of permutations and is looking for them everywhere!A permutation in this problem is a sequence of integers p_1, p_2, \dots, p_k such that every integer from 1 to k occurs exactly once in it. For example, the following sequences are permutations of [3, 1, 4, 2], [1] and [6, 1, 2, 3, 5, 4]. The following sequences are not permutations: [0, 1], [1, 2, 2], [1, 2, 4] and [2, 3].In the lobby of the company's headquarter statistics on visits to the company's website for the last n days are published — the sequence a_1, a_2, \dots, a_n. Polycarp wants to color all the elements of this sequence in one of three colors (red, green or blue) so that:  all red numbers, being written out of a_1, a_2, \dots, a_n from left to right (that is, without changing their relative order), must form some permutation (let's call it P);  all green numbers, being written out of a_1, a_2, \dots, a_n from left to right (that is, without changing their relative order), must form the same permutation P;  among blue numbers there should not be elements that are equal to some element of the permutation P. Help Polycarp to color all n numbers so that the total number of red and green elements is maximum.InputThe first line contains an integer n (1 \le n \le 2\cdot10^5) — the length of the sequence a. The second line contains n integers a_1, a_2, \dots, a_n (1 \le a_i \le 2\cdot10^5).OutputPrint a string s of length n such that:  s_i='R', if the element a_i must be colored in red;  s_i='G', if the element a_i must be colored in green;  s_i='B', if the element a_i must be colored in blue. The string s should maximize the total number of red and green elements when fulfilling the requirements from the main part of the problem statement. If there are several optimal answers, print any of them.ExamplesInput
5
1 2 3 2 1
Output
RBBBG
Input
3
1 1 1
Output
BBB
Input
10
3 3 2 2 5 4 1 5 4 1
Output
RGRGRRRGGG
Input
10
3 9 3 1 2 1 2 4 4 4
Output
RBGRRGGBBB

5
1 2 3 2 1

RBBBG 
['*special problem', 'binary search', 'greedy', '*2000']