题目描述

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.

输入格式

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!

输出格式

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.

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

提示

没有写明提示

题目来源

By 镇海中学 鸣谢David Lee重新制作数据