Cartesian Tree

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

Let us consider a special type of binary search trees, called cartesian trees. Recall that a binary search
tree is a rooted ordered binary tree, such that for its every node x the following condition is satisfied:
each node in its left subtree has the key less than the key of x, and each node in its right subtree has the
key greater than the key of x.
That is, if we denote the left subtree of the node x by L(x), its right subtree by R(x) and its key by
kx , for each node x we will have
• if y ∈ L(x) then ky < kx
• if z ∈ R(x) then kz > kx
The binary search tree is called cartesian if its every node x in addition to the main key kx also has
an auxiliary key that we will denote by ax , and for these keys the heap condition is satisfied, that is
• if y is the parent of x then ay < ax
Thus a cartesian tree is a binary rooted ordered tree, such that each of its nodes has a pair of two
keys (k, a) and three conditions described are satisfied.
Given a set of pairs, construct a cartesian tree out of them, or detect that it is not possible.
 

Input

 The first line of the input file contains an integer number N — the number of pairs you should build
cartesian tree out of (1 ≤ N ≤ 50 000). The following N lines contain two integer numbers each — given
pairs (ki , ai ). For each pair |ki |, |ai | ≤ 30 000. All main keys and all auxiliary keys are different, i.e.
ki = kj and ai = aj for each i = j.
 

Output

 On the first line of the output file print YES if it is possible to build a cartesian tree out of given pairs
or NO if it is not. If the answer is positive, output the tree itself in the following N lines. Let the nodes
be numbered from 1 to N corresponding to pairs they contain as these pairs are given in the input file.
For each node output three numbers — its parent, its left child and its right child. If the node has no
parent or no corresponding child, output 0 instead.
If there are several possible trees, output any one.
 

Sample Input

7
5 4
2 2
3 9
0 5
1 3
6 6
4 11

Sample Output

YES
2 3 6
0 5 1
1 0 7
5 0 0
2 4 0
1 0 0
3 0 0

Hint

 

Source