Ethan Hunt's Mission

Ethan Hunt, the hero of the "Mission Impossible" series, is renowned for his skills as a saboteur. However, there was an instance when the CIA enlisted him to evaluate the reliability of their door codes. As depicted in popular films, CIA code locks are typically opened using a magnetic card. Let's assume this card holds a sequence of bits of length (M). When these bits are read, if they match the door code, the door unlocks. When asked how he would breach such a lock, Hunt suggested the following approach.

Imagine a long magnetic tape on which we record an arbitrary sequence of length (N) ((N $\ge$ M)), composed of 0s and 1s, with each bit having an equal probability of being 0 or 1. We then pass this tape through the lock. If the lock code appears anywhere in this sequence, the lock will open. (Note: This scenario is set in a Hollywood movie, so the mismatch between the physical encoding of a continuous tape and a magnetic card is not a concern.)

The CIA's leadership decided to evaluate all lock codes for their resistance to Hunt's method.

Input

The first line contains the number (N) - the length of the bit sequence recorded on the tape ((1 $\le$ N $\le$ 60)). The second line contains the lock code, a non-empty string of characters "0" and "1", whose length does not exceed (N).

Output

Output the probability that the lock code appears in a randomly generated sequence of bits of length (N). The probability should be presented as an irreducible fraction, with the numerator and denominator separated by the symbol "/".

Examples