Problem name: Find the map

Problem ID: 19007

Problem setter: Stefan Ciobaca

Problem input: standard input

Problem output: standard output

Background:

The map of the lost city has been lost. There is only little information left. It is a known fact that the map contained N important points. Any two of them could have been connected using a one way link (e.g. if point A was connected to point B, point B wasn't necesarely connected to point A). Also there may be at most one connection from point A to point B.

You have found some more information about the map. You know for each of the N important points exactly how many points were connected to it and how many points it was connected to. You are thinking about making lots of money by selling a reconstruction the map.

Problem:

So you should write a program, that, given the above information, will construct a version of the map (there may be more solutions, your program will only need to find one).

Input data:

The first line contains number N, the number of important points. The points are numbered from 1 up to N.

On line I + 1, I = 1,N, you will find two space separated values: the first number DI[i] is the number of important points which are connected to point I and the second one DE[I] is the number of important points to which point I is connected.

Output data:

If there is no solution (the information you got must have been fake) you will only write one line with a -1. Otherwise, you should write:

On the first line, the number of connections M.

On the next M lines, you will write two number A and B, meaning that point A is connected to point B.

Example:

input:

4
2 1
0 2
2 1
1 1

output:

5
2 1
3 1
2 3
4 3
1 4

Restrictions:

• 1 <= N <= 100
• There can't be a link between a point to itself
• 0 <= DI[i], DE[i] <= 100, for i=1,N
• Time limit: 1 second
• Output limit: 1 MB
• Data limit: 1 MB
• Stack limit: 1 MB