The 3n + 1 problem

Sample Problems

Consider the following algorithm to generate a sequence of numbers. Start with an integer n. If n is even, divide by 2. If n is odd, multiply by 3 and add 1. Repeat this process with the new value of n, terminating when n = 1. For example, the following sequence of numbers will be generated for n = 22:

22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

It is conjectured (but not yet proven) that this algorithm will terminate at n = 1 for every integer n. Still, the conjecture holds for all integers up to at least 1, 000, 000.

For an input n, the cycle-length of n is the number of numbers generated up to and including the 1. In the example above, the cycle length of 22 is 16. Given any two numbers i and j, you are to determine the maximum cycle length over all numbers between i and j, including both endpoints.

Input

The input will consist of a series of pairs of integers i and j, one pair of integers per line. All integers will be less than 1,000,000 and greater than 0.

Output

For each pair of input integers i and j, output i, j in the same order in which they appeared in the input and then the maximum cycle length for integers between and including i and j. These three numbers should be separated by one space, with all three numbers on one line and with one line of output for each line of input.

Sample Input

1 10

100 200

201 210

900 1000

Sample Output

1 10 20

100 200 125

201 210 89

900 1000 174

Sample C++ Program

Problem: WERTYU










A common typing error is to place the hands on the keyboard one row to the right of the correct position. So "Q" is typed as "W" and "J" is typed as "K" and so on. You are to decode a message typed in this manner.

Input consists of several lines of text. Each line may contain digits, spaces, upper case letters (except Q, A, Z), or punctuation shown above [except back-quote (`)]. Keys labelled with words [Tab, BackSp, Control, etc.] are not represented in the input. You are to replace each letter or punction symbol by the one immediately to its left on the QWERTY keyboard shown above. Spaces in the input should be echoed in the output.

Sample Input

O S, GOMR YPFSU/

Output for Sample Input

I AM FINE TODAY.

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Assembly Language

Sample Program

name "calc-sum"

org 100h ; directive make tiny com file.

; calculate the sum of elements in vector,
; store result in m and print it in binary code.

; number of elements:
mov cx, 5

; al will store the sum:
mov al, 0

; bx is an index:
mov bx, 0

; sum elements:
next: add al, vector[bx]

; next byte:
inc bx

; loop until cx=0:
loop next


; store result in m:
mov m, al


; print result in binary:
mov bl, m
mov cx, 8
print: mov ah, 2 ; print function.
mov dl, '0'
test bl, 10000000b ; test first bit.
jz zero
mov dl, '1'
zero: int 21h
shl bl, 1
loop print
; print binary suffix:
mov dl, 'b'
int 21h



mov dl, 0ah ; new line.
int 21h
mov dl, 0dh ; carrige return.
int 21h


; print result in decimal:
mov al, m
call print_al




; wait for any key press:
mov ah, 0
int 16h



ret

; variables:
vector db 5, 4, 5, 2, 1
m db 0


print_al proc
cmp al, 0
jne print_al_r
push ax
mov al, '0'
mov ah, 0eh
int 10h
pop ax
ret
print_al_r:
pusha
mov ah, 0
cmp ax, 0
je pn_done
mov dl, 10
div dl
call print_al_r
mov al, ah
add al, 30h
mov ah, 0eh
int 10h
jmp pn_done
pn_done:
popa
ret
endp