P10164 [DTCPC 2024] Gob

For a $01$ sequence $\{a_n\}$, find the minimum $k$ such that there exists a set $\{(l_k,r_k)\}$ that satisfies the following condition. - $\forall i\in[1,n]$, $a_i=1$ if and only if $\exist j\in[1,k]$, $i\in[l_j,r_j]$. It can be proven that the set $\{(l_k,r_k)\}$ that satisfies the condition is unique. A $01$ sequence $\{a_n\}$ is good if and only if $\forall i\in[1,k)$, $r_i-l_i

One line containing a $01$ sequence $\{a_n\}$ of length $n$ ($n\leq 800$).

One line containing one number, which is the answer.

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