[Usaco2011 Feb]The Lost Cows

时间限制:10s      空间限制:128MB

题目描述


One sunny day farmer John was kidnapped by evil farmer Marcus's
cows. FJ wasn't too concerned about his forced holiday but wanted
to make sure that his cows got home safely together.

The cows are spread out in every one of FJ's N (3 <= N <= 200)
pastures conveniently numbered 1..N. The barn is located at pasture
1. The farm has an interesting navigation system: at every pasture
i there are M (1 <= M <= 200) signs S_ij (1 <= S_ij <= N) which one
could reference as S_i1..S_iM; each sign points the way to a pasture.
Sometimes a sign points to a path that leads back to the same
pasture.

Farmer Marcus's cows allow FJ to write a single message to all of
his cows. FJ's plan is to write a list of sign numbers such that
any cow who follows those instructions will all arrive at the barn
when each cow has completed all the instructions.

When a cow starts at a given pasture then she will first follow the
path indicated by the first sign number on FJ's list. When she
arrives at the second pasture, she looks at the second sign of FJ's
list and follows the path marked by that sign. She continues until
she exhausts the instruction list, at which point she should be at
the barn.

Find a list of instructions containing no more than 5,000,000 sign
numbers that will guide every cow, from every pasture, to the barn
after all instructions are followed.  It is guaranteed that such a
list exists.

Consider a set of three signs in four pastures that direct the cows
like these do:
                               ** Pasture# **
                              1    2    3    4
                     Sign 1   4    4    1    3
                     Sign 2   1    3    2    4
                     Sign 3   4    2    3    1

The set of instructions below will direct cows to the barn from any
of the four pastures:

       Instruction#   Sign#            Instruction#   Sign#
            1           1                   5           3
            2           2                   6           1
            3           1                   7           3
            4           2

The cow in pasture 1 will read sign #1 at time 1 and be directed
to pasture 4.  At time 2, she is in pasture 4 and (per FJ's
instructions) read sign #2 and then be directed to pasture 4. Below
is a table that shows the cow's travels:

                  * * * *  Cow in pasture  1  * * * *

        Time    CurrentPasture#    WhichSign     Sign->Nextpasture
          1            1               1                4
          2            4               2                4 (same pasture!)
          3            4               1                3
          4            3               2                2
          5            2               3                2 (same pasture)
          6            2               1                4
          7            4               3                1 Barn!

Similarly: Pasture 2's cow visits pastures [2]-4-4-3-2-2-4-1.
           Pasture 3's cow visits pastures [3]-1-1-4-4-1-4-1.
           Pasture 4's cow visits pastures [4]-3-2-4-4-1-4-1.

Given a set of signs, create a set of instructions.


输入格式


* Line 1: Two space separated integers: N and M

* Lines 2..M+1: Line i+1 describes the contents of each pasture's N
        signs with N integers: S_1i..S_Ni


输出格式


* Lines 1..?: The sign numbers the cows should follow, one per line.


样例输入

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



样例输出

1
2
1
2
3
1
3


提示

没有写明提示


题目来源

Gold