Restore a Binary Search Tree

Chansol built a binary search tree in which each of the $N$ nodes holds an integer. In a binary search tree, for every node $i$, every number in the left subtree of $i$ is less than the number in $i$, and every number in the right subtree of $i$ is greater than the number in $i$.

For every $i$, Chansol recorded the depth $H_i$ of node $i$ and the integer $A_i$ written on node $i$. All $A_i$ are distinct, and the root has depth 1. ($1 \le i \le N$)

Chansol lost the tree while attending the ICPC World Finals. Restore the binary search tree from the recorded information.

The first line contains the number of nodes $N$. ($1 \le N \le 200000$)

The next $N$ lines describe the nodes. For each $1 \le i \le N$, line $(i+1)$ contains the integer $A_i$ written on node $i$ and the depth $H_i$ of node $i$, separated by a space. ($-2 \cdot 10^9 \le A_i \le 2 \cdot 10^9$, $1 \le H_i \le N$) All $A_i$ are distinct.

If the recorded information cannot be restored to a binary search tree, print -1.

Otherwise, print the structure of the tree over $N$ lines. Line $i$ contains the node numbers of the left child and the right child of node $i$. If a child does not exist, print -1 in its place.

If several trees can be restored, print any of them.