Hermoine and Magic potion

Hermoine wants to make a magic potion.The recipe to make the potion is in a magic book which will open only if she solves this puzzle. There is a binary non decreasing string S.Starting from an empty string find minimum number of times (N) string S needs to be appended such that the length of longest non decreasing subsequence of the newly obtained string is atleast L.Help Hermoine to solve the pu