Make Length 1

You are given a binary string $S$ of length $N$. You can perform the following operation on $S$: - Select an index $i \ (1 \leq i \lt |S|)$ such that $S_i=S_{i+1}$. - Set $S_i$ to $0$ and remove $S_{i+1}$ from the string. Note that after each operation, the length of $S$ decreases by $1$. Is it possible to reduce $S$ to a single character by performing the mentioned operation **exactly** $N-1$