The character distribution of the encoded message for the example ("THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG"):

    8: " " (note that the original also has 8 spaces)
    4: "O"
    3: "E"
    2: "H", "R", "T", "U"
    1: "Z", "B", "Y", "N", "C", "D", "X", "M", "P",
       "W", "F", "Q", "G", "L", "S", "A", "I", "K",
       "J", "V"

The character distribution of the encoded message (to be solved):

    12: ";", " ", "I"
    11: "H"
    10: "*", "-", "F", "2"
     9: "?", "S", "L", "O", "E", "T"
     8: "N", "4", "W"
     7: "3", "(", "J", "#", "/", "U"
     6: "C", ">", "<", """, "D", "A", ".", "%", "0"
     5: "9", "V", "@", "+", "$", "Y", "G", "6"
     4: "=", ":", "Z", "P", "R", "&", "7", "1", "B",
        ",", "!"
     3: "8", ")", "K", "X", "'", "5"
     2: "Q", "M"