Problem A: User-Friendly Manuals

Manuals are often difficult to read because of the order in which new concepts appear. Let us assume that the part of the manuals we are interested in is a permutation of a set of entries.

An entry has a (unique) keyword and a description, which can explicitly refer to other entries. We say that an entry e₂ depends on an entry e₁ when the description of e₂ mentions e₁. If that is the case, e₁ must occur before e₂ in the permutation, that is, e₁ is printed before e₂. Remark that dependencies between entries are cycle-free.

For the sake of readability, two additional rules are considered to define the user-friendliest permutation of a set of entries. Let then e₁ and e₂ be two entries that could be printed at some point according to the existent dependencies.

1. First, ties are broken by dependency proximity.
   For every entry e, let δ(e) be the set of entries on which e depends. Entry e₁ is printed before e₂ if there is an entry e'₁ ∈ δ(e₁) that occurs after any entry e'₂ ∈ δ(e₂) in the permutation.

2. Then, ties are broken by keyword order.
   If rule (a) was not decisive and there is still a tie between e₁ and e₂, e₁ is printed before e₂ provided the keyword of e₁ is less than the keyword of e₂.

Let us see an example with the entries and the dependencies depicted in the figure bellow. From now on, entry descriptions are omitted and entry keywords are integers (and compared as integers in the context of rule (b)). An edge from e₁ to e₂ means that e₂ depends on e₁.

The following table shows that 0 1 2 6 is the beginning of the corresponding user-friendliest permutation. Since entries 0, 1, 3 and 8 do not depend on any entry, rule (a) cannot determine the first two selections, which are justified by rule (b). The third selection is entry 2 because 2 depends on 1, 1 was the previous selection, and all the entries on which 3 (respectively, 8) depends, which are none, appear before 1. Then, when dependencies allow 3, 6, 7 and 8 to be chosen, rule (a) eliminates entries 3 and 8, and the tie between 6 and 7 is broken by rule (b).

Task

Input

The first line of the input contains two integers, E and D, separated by a single space. E is the number of entries and D is the number of dependencies. Entries are identified by integers, ranging from 0 to E − 1.

Each of the following D lines contains two integers, e₁ and e₂, which indicate that entry e₂ depends on entry e₁. The two integers are separated by a single space.

Output

Constraints

• 2 ≤ E ≤ 5 000
• 1 ≤ D ≤ 30 000

Input example

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

Output example

0 1 2 6 7 3 4 8 5 9