Optimisation 

A company decides to simulate on computer the process of manufacturing its own goods. In order to do that, it makes the following observations:

1.

The whole process can be splitted into several steps; between them there are some dependencies. This can be represented by a diagram (graph), which we suppose to be only one for all goods produced by company as in figure 1;

2.

First step designates the start of manufacturing process;there is only one first step, denoted by the number 1;

3.

There are not steps isolated or outside the process (every step is linked by a path with the first step);

4.

Some steps are total dependants; so, we claim that the step i is total dependant of step j if every path in the fabrication process cannot arrive to i without was passing through j.

So, all steps are total dependants of step 1.

Example: In the process shown by the figure 1 the step 4 is total dependant of step 3, steps 5,6 and 7 are total dependants of 4 (hence of 3), but step 3 is not total dependant of step 2.

The Computing Center Dept. of company notes that whole manufacturing process is easier to be controlled if it would be structured by a tree, as follows:

• All steps of manufacturing process are nodes of the tree;
• Each node ensures total dependence of all its own descendants;

The tree associated to the diagram from figure 1 is shown in figure 2.

Your task is to write a program that builds this dependence tree.

Input 

The input file contains several input data sets. An input data set has the following format:

n - number of steps of manufacturing process ( $2 \le n \le 99$);

a11	a12	$\dots$	a1n
a21	a22	$\dots$	a2n
$\vdots$	$\vdots$	$\ddots$	$\vdots$
an1	an2	$\dots$	ann

where a_ij=1 if step j follows directly step i in the process diagram, otherwise a_ij=0.

Output 

At output, the program must write n-1 lines for every input data set; each line has the format:

$i \ j$

with the meaning that node j is a direct descendant of node i in the tree. The pair (i₁ j₁) follows (i₂ j₂) if and only if (i₁<i₂) or (i₁=i₂ and j₁<j₂).

Sample Input 

10
0 1 1 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
0 0 1 0 1 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0
0 0 1 0 0 0 0 0 1 1
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0

Sample Output 

1 2
1 3
3 4
4 5
4 6
4 7
7 8
8 9
8 10