# ([1], county level olympiad, 1994) Count the number of correct bracket sequences of length 2n.
# (10th grade math course) Count the number of paths on a grid going from 1,1 to n, m. At each step you can either increase your x coordinate or increase your y coordinate.
# Given a permutation of numbers 1 to n, what's the minimum number of swaps one can use to get to the identity permutation.

# Count the number of size n permutations such that p^2(i) = i for all i in {1..n}.

# ([1], 'infoarena':problema/perm2) Given a permutation p what's the minimum k so that p^k(i) = i for all i in {1..n}.
# (romanian IOI selection 99, topcoder 2004, 'infoarena':problema/perm5) Find a permutation p of n elements which maximizes k so that p^k(i) = i for all i in {1..n}.
# ([1]) 6 people are at a party. Each two persons can be either friends or enemies. Prove that there is at least a group of three mutual friends or a group of three mutual enemies.