TOPOSORT - Topological Sorting

Sandro is a well organised person. Every day he makes a list of things which need to be done and enumerates them from 1 to n. However, some things need to be done before others. In this task you have to find out whether Sandro can solve all his duties and if so, print the correct order.

Input

In the first line you are given an integer n and m (1 <= n <= 10000, 1 <= m <= 1000000). On the next m lines there are two distinct integers x and y, (1 <= x, y <= 10000) describing that job x needs to be done before job y.

Output

Print "Sandro fails." if Sandro cannot complete all his duties on the list. If there is a solution print the correct ordering, the jobs to be done separated by a space. If there are multiple solutions print the one, whose first number is smallest, if there are still multiple solutions, print the one whose second number is smallest, and so on.

Example 1

Input:
8 9
1 4
1 2
4 2
4 3
3 2
5 2
3 5
8 2
8 6

Output:
1 4 3 5 7 8 2 6 

Example 2

Input:
2 2
1 2
2 1

Output:
Sandro fails.

Added by:Josef Ziegler
Date:2011-10-23
Time limit:0.5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All

hide comments
2014-10-20 18:57:01 Siddhant Garule
I am getting WA with 12th test case. Plz provide some more test cases
2014-08-29 15:37:24 Durga Tiwari
I was getting TLE , tried fast input/output and AC
2013-12-03 23:39:25 arthur
No java solution
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