Problem 2: The Great
Escape, *(K Narayan Kumar, CMI)*

Heroes in Indian movies are capable of superhuman feats. For example, they can jump between buildings, jump onto and from running trains, catch bullets with their hands and teeth and so on. A perceptive follower of such movies would have noticed that there are limits to what even the superheroes can do. For example, if the hero could directly jump to his ultimate destination, that would reduce the action sequence to nothing and thus make the movie quite boring. So he typically labours through a series of superhuman steps to reach his ultimate destination.

In this problem, our hero has to save his wife/mother/child/dog/... held captive by the nasty villain on the top floor of a tall building in the centre of Bombay/Bangkok/Kuala Lumpur/.... Our hero is on top of a (different) building. In order to make the action "interesting" the director has decided that the hero can only jump between buildings that are "close" to each other. The director decides which pairs of buildings are close enough and which are not.

Given the list of buildings, the identity of the building where the hero begins his search, the identity of the building where the captive (wife/mother/child/dog...) is held, and the set of pairs of buildings that the hero can jump across, your aim is determine whether it is possible for the hero to reach the captive. And, if he can reach the captive he would like to do so with minimum number of jumps.

Here is an example. There are 5 buildings, numbered
*1,2,...,5*, the hero stands on building *1* and the
captive is on building *4*. The director has decided that
buildings *1* and *3*, *2* and *3*,
*1* and *2*, *3* and *5* and *4*
and *5* are close enough for the hero to jump across. The hero
can save the captive by jumping from *1* to *3* and then
from *3* to *5* and finally from *5* to
*4*. (Note that if *i* and *j* are close then
the hero can jump from *i* to *j* as well as from
*j* to *i*.). In this example, the hero could have also
reached *4* by jumping from *1* to *2*,
*2* to *3*, *3* to *5* and finally from
*5* to *4*. The first route uses *3* jumps while
the second one uses *4* jumps. You can verify that *3*
jumps is the best possible.

If the director decides that the only pairs of buildings that are
close enough are *1* and *3*, *1* and *2*
and *4* and *5*, then the hero would not be able to
reach building *4* to save the captive.

Input format

The first line of the input contains two integers *N* and
*M*. *N* is the number of buildings: we assume that our
buildings are numbered *1,2,...,N*. *M* is the number
of pairs of buildings that the director lists as being close enough to
jump from one to the other. Each of the next *M* lines, lines
*2,...,M+1*, contains a pair of integers representing a pair of
buildings that are close. Line *i+1* contains integers
*Ai* and *Bi*, *1 ≤ Ai ≤ N* and *1 ≤
Bi ≤ N*, indicating that buildings *Ai* and *Bi*
are close enough. The last line, line *M+2* contains a pair of
integers *S* and *T*, where *S* is the building
from which the Hero starts his search and *T* is the building
where the captive is held.

Output format

If the hero cannot reach the captive print *0*. If the
hero can reach the captive print out a single integer indicating the
number of jumps in the shortest route (in terms of the number of
jumps) to reach the captive.

Test Data:

You may assume that *1 ≤ N ≤ 3500* and *1 ≤ M
≤ 1000000*. Further, in at least *50%* of the inputs
*1 ≤ N ≤ 1000* and *1 ≤ M ≤ 200000*.

Example:

Here are the inputs and outputs corresponding to the two examples discussed above.

Sample Input 1:

5 5 1 3 2 3 1 2 3 5 4 5 1 4

Sample Output 1:

3

Sample Input 2:

5 3 1 3 1 2 4 5 1 4

Sample Output 2:

0

Test data:

CPU Timelimit: | 3 seconds |

Memory limit: | 64M |

Grading style: | ioi |