Huffman Codes

Author: @037

Compile

sudo g++ -std=c++11 -o Huffman.exe Huffman.cpp

Description

Suppose that we have to store a sequence of symbols (a file) efficiently, namely we want to minimize the amount of memory needed. For the sake of simplicity we assume that the symbols are restricted to the first 6 letters of the alphabet.

Input structure

The input consists of 6 integers, one per each line. Each integer represents the frequency of characters, A, B, C, D, E, and F, in this order.

Output structure

Output is the the decision about which tree goes to the left and which one goes to the right. The final tree is unique.

Example

Input

15
11
5
1
2
4

Output

A:0
B:10
C:110
D:11100
E:11101
F:1111