Binary Search Heap Construction

Time Limit: 5 Seconds
Memory Limit: 32768 KB

Read the statement of problem G for the definitions concerning trees. In the
following we define the basic terminology of heaps. A **heap** is a tree
whose internal nodes have each assigned a **priority** (a number) such that
the priority of each internal node is less than the priority of its parent. As a
consequence, the root has the greatest priority in the tree, which is one of the
reasons why heaps can be used for the implementation of priority queues and for
sorting.

A binary tree in which each internal node has both a label and a priority,
and which is both a binary search tree with respect to the labels and a heap
with respect to the priorities, is called a **treap**. Your task is, given a
set of label-priority-pairs, with unique labels and unique priorities, to
construct a treap containing this data.

**Input Specification**

The input contains several test cases. Every test case starts with an integer
*n*. You may assume that *1<=n<=50000*. Then follow *n*
pairs of strings and numbers
*l*_{1}/p_{1},...,l_{n}/p_{n} denoting the
label and priority of each node. The strings are non-empty and composed of
lower-case letters, and the numbers are non-negative integers. The last test
case is followed by a zero.

**Output Specification**

For each test case output on a single line a treap that contains the
specified nodes. A treap is printed as *(<left
sub-treap><label>/<priority><right sub-treap>)*. The
sub-treaps are printed recursively, and omitted if leafs.

**Sample Input**

7 a/7 b/6 c/5 d/4 e/3 f/2 g/1
7 a/1 b/2 c/3 d/4 e/5 f/6 g/7
7 a/3 b/6 c/4 d/7 e/2 f/5 g/1
0

**Sample Output**

(a/7(b/6(c/5(d/4(e/3(f/2(g/1)))))))
(((((((a/1)b/2)c/3)d/4)e/5)f/6)g/7)
(((a/3)b/6(c/4))d/7((e/2)f/5(g/1)))

Source:

**University of Ulm Local Contest 2004**
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