Description

Teacher Mai has a multiplication table in base p.

For example, the following is a multiplication table in base 4:

• 0 1 2 3

0 00 00 00 00

1 00 01 02 03

2 00 02 10 12

3 00 03 12 21

But a naughty kid maps numbers 0..p-1 into another permutation and shuffle the multiplication table.

For example Teacher Mai only can see:

11=11 13=11 12=11 10=11

31=11 33=13 32=12 30=10

21=11 23=12 22=31 20=32

01=11 03=10 02=32 00=23

Teacher Mai wants you to recover the multiplication table. Output the permutation number 0..p-1 mapped into.

It's guaranteed the solution is unique.

Format

Input

There are multiple test cases, terminated by a line "0".

For each test case, the first line contains one integer p(2<=p<=500).

In following p lines, each line contains 2p integers.The (2j+1)-th number x and (2j+2)-th number y in the i-th line indicates equation ij=xy in the shuffled multiplication table.

Warning: Large IO!

Output

For each case, output one line.

First output "Case #k:", where k is the case number counting from 1. The following are p integers, indicating the permutation number 0..p-1 mapped into.

Samples

4
2 3 1 1 3 2 1 0
1 1 1 1 1 1 1 1
3 2 1 1 3 1 1 2
1 0 1 1 1 2 1 3
0

Case #1: 1 3 2 0

Limitation