The Černý Conjecture on Synchronizing Words

A deterministic finite automaton (DFA) is a tuple $M = (Q, \Sigma, \delta)$ where $Q$ is a finite set of states, $\Sigma$ is an alphabet, and $\delta : Q \times \Sigma \to Q$ is a transition function. A synchronizing word (or reset word) for a DFA is a word $w \in \Sigma^*$ such that there exists a single state $p \in Q$ with the property that reading $w$ from any state $q \in Q$ leads to $p$; formally, $\delta^*(q, w) = p$ for all $q \in Q$, where $\delta^*$ denotes the extension of $\delta$ to words. A DFA is called synchronizing if it admits at least one synchronizing word. Prove or disprove: For every synchronizing DFA with $n$ states, there exists a synchronizing word of length at most $(n - 1)^2$.