Problem 2C
Letter Selection

Description

Consider all possible selections (combinations) of the letters A, B and C :

A, AB, ABC, AC, B, BC, and C. Here they are sorted into dictionary order. If each selection is assigned an index then the selections correspond to the following indices.

1A
2AB
3ABC
4AC
5B
6BC
7C
  
There are two parts to the problem:
Firstly you must find the index for a particular selection of letters. For example the index of the selection AC is 4.
Secondly, you must find a selection n units below this. For example if n = 2, then the required selection is BC (two below AC).

Input

The input will be three lines. The first line will be a number, k, (1 <= k <= 26), the number of letters in the selection. The selection will be made of the first k letters of the alphabet. (E.g. k = 5, then selections will be made of the five letters, A, B, C, D, and E.) The next line contains a particular selection. You will have to find its index.

The last line contains a number, n, (0 <= n <= 30000). Add n to the index just found and find the corresponding selection.

Output

The output will be one line containing the index of the selection, and another line containing a selection corresponding to the modified index.

Example 1

Input

3
AC
2

Output

4
BC

(4 is the index of AC, BC is the selection 2 below it.)

Example 2

Input

4
AC
3

Output

6
B