Cartesian Tree

Time Limit: 10 Seconds    Memory Limit: 32768 KB
Special Judge

Let us consider a special type of a binary search tree, called a cartesian tree. 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 then the key of x, and each node in its right subtree has the key greater then the key of x.

That is, if we denote left subtree of the node x by L(x), its right subtree by R(x) and its key by k_x, then for each node x we have

• if y L(x) then k_y < k_x
• if z R(x) then k_z > k_x

The binary search tree is called cartesian if its every node x in addition to the main key k_x also has an auxiliary key that we will denote by a_x, and for these keys the heap condition is satisfied, that is

• if y is the parent of x then a_y < a_x

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

Input consists of multiple test cases.
For each case, the first line contains an integer N -- the number of pairs you should build cartesian tree out of (1 N 50 000). The following N lines contain two numbers each -- given pairs (k_i, a_i). For each pair |k_i|, |a_i| 30 000. All main keys and all auxiliary keys are different, i.e. k_i k_j and a_i a_j for each i j.

Output

For each test case, print in the first line 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, on the following N lines output the tree. Let nodes be numbered from 1 to N corresponding to pairs they contain as they 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

Submit

Source: Northeastern Europe 2002, Northern Subregion