Problem D

                  Growing trees from numbers


Trees  in  this  problem are abstract entities, not  biological
species.  Sorry  about that. We shall consider only  so  called
rooted  trees  which   consist of a set of nodes  connected  by
links in such
a  way  that  each  node, except one (called  root  node),  has
exactly one predecessor (called parent node), and any number of
successor nodes (called child nodes). If a node has no children
it  is  called terminal node. We can also define a rooted  tree
recursively as the root node and a number of subtrees connected
to the root.
Suppose we have a rooted tree T. We can encode the tree into  a
positive integer G(T) as follows (Goebel encoding).

1.  If the tree is trivial, i.e. contains only the root:

    G(T) = 1

2.  If  T has the form of  T = root(T1, ... ,Tk), where T1,...,
Tk  are subtrees connected to the root:

    G(T) = P(G(T1)) * ... * P(G(Tk))

     P(i) above denotes i-th prime number; asterisk '*' denotes
multiplication. Recall, P(1)=2,
    P(2)=3, P(3)=5, P(4)=7, and so on.

Input
You  are  asked  to write a program that reads  a  sequence  of
positive  integers  from the standard input  stream,  considers
each  input number as encoded representation of a rooted  tree,
and  generates  the textual form of the tree encoding  process.
Last  number in the input sequence is 0; it will terminate  the
program execution. Input numbers are in the range 0..65535  (16
bits unsigned).

Output
To be specific, the following example gives the expected output
of  the  program. The root node for a tree encoded by number  n
has  always  the  form  ':n>'.  Other  nodes  are  printed   as
''. Tree structure is represented by simple  horizontal
and vertical connectors.
EXAMPLE

Input

1 3 35 999 0

Output

:1>

:3>--<3:2>--<2:1>

:35>--<5:3>--<3:2>--<2:1>
   |
   |--<7:4>--<2:1>
          |
          |--<2:1>

:999>--<3:2>--<2:1>
    |
    |--<3:2>--<2:1>
    |
    |--<3:2>--<2:1>
    |
    |--<37:12>--<2:1>
             |
             |--<2:1>
             |
             |--<3:2>--<2:1>

                             TEST
input        1 3 35 999 470 540 71 0
output

:1>

:3>--<3:2>--<2:1>

:35>--<5:3>--<3:2>--<2:1>
   |
   |--<7:4>--<2:1>
          |
          |--<2:1>

:999>--<3:2>--<2:1>
    |
    |--<3:2>--<2:1>
    |
    |--<3:2>--<2:1>
    |
    |--<37:12>--<2:1>
             |
             |--<2:1>
             |
             |--<3:2>--<2:1>

:470>--<2:1>
    |
    |--<5:3>--<3:2>--<2:1>
    |
    |--<47:15>--<3:2>--<2:1>
             |
             |--<5:3>--<3:2>--<2:1>

:540>--<2:1>
    |
    |--<2:1>
    |
    |--<3:2>--<2:1>
    |
    |--<3:2>--<2:1>
    |
    |--<3:2>--<2:1>
    |
    |--<5:3>--<3:2>--<2:1>

:71>--<71:20>--<2:1>
            |
            |--<2:1>
            |
            |--<5:3>--<3:2>--<2:1>

#include 
#define LMX 11
#define PMX 6543

/* PROTOTYPY FUNKCJI */
void     GenTree(unsigned n,int cp);
void     VerticalLines(void);
void     np(unsigned n, unsigned *q, unsigned *i);
void     generate(int i);
unsigned prime(int i);
int tv[LMX];
int mtv=0;
unsigned tp[PMX] = {1,2,3,5};
int mtp = 3;

unsigned prime(int i)
{ unsigned pp, k, n=tp[mtp];

  if(i<1 || i>=PMX) return 1;

  while (mtp",n);
  if (n==1) putchar('\n');
  else
  { np(n,&q,&i);
    tv[++mtv]=cp+l;
    do
    { l1 = printf("--<%u",q);
      if(q==n) --mtv;
      GenTree(i,cp+l+l1);
      n/=q;
      if(n>1)
      { np(n,&q,&i);
        VerticalLines(); putchar('\n');
        if(n!=q) VerticalLines(); else VerticalLines();
      }
    } while (n>1);
  }
}

void VerticalLines()
{ int i,j,k;

  for(j=0,i=1; i<=mtv; i++)
  { k=tv[i];
    printf("%*c",k-j,'|');
    j=k;
  }
}

void np(unsigned n,unsigned *q,unsigned *i)
{ *i=1; *q=2;
  while(n % *q != 0) *q=prime(++(*i));
}