Given a bracket sequence of length 1200, (i.e. a string s = s_0, s_1, \dots s_{1199} containing only ‘(‘ and ‘)’) with exactly 1000 open brackets and 200 close brackets, what is the maximum possible number of cyclic permutations of the string s that are open bracket sequences ?
A bracket sequence is said to be open, if for every prefix of the sequence, the number of open brackets is strictly more than, the number of close brackets.
An open bracket sequence can be made into a correct bracket sequence by adding some closing brackets to the end, and no prefix of the sequence is a correct bracket sequence.
A cyclic permutation of the string s_0s_1\dots s_{n-1} is a string s_i s_{i+1}\dots s_{n-1}s_0 s_1 \dots s_{i-1} , i.e. the elements of the string are shifted cyclically.
There are exactly n cyclic permutations of the string s
ans -800
Please expalin this problm.