3. Railway turnout

Problem description

It's known fact that all railway stations have special turnout system to rearrange wagons of train (see the figure). Train with N wagons numbered from 1 to N in increasing order comes to turnout from the right side. Railway station workers want to rearrange wagons so that at the left side of turnout they appear in a given order p₁, p₂, ..., p_n. Employees can perform exactly 3 operations:
A. Put wagon into turnout;
B. Take wagon from the left side of turnout;
C. Take wagon from the right side of turnout, see figure and example.

Write a program which will help railway station workers!

Input

There is one number N on the first line (1 <= N <= 250). On the second line there are N positive integers p₁, p₂, ..., p_n, which form a permutation of numbers from 1 to N .

Output

Write NO in the first line of output if it's impossible to rearrange wagons in given order. Otherwise write YES on the first line and sequence of operations which must be performed on the second line encoded with letters A, B and C. If there are several solutions output any of them.

Example