The Only Mode

You are given an array of integers $A$ of size $N$ (indexed from $1$ to $N$) where $A\_i$ is either $0$, $1$, $2$, or $3$.

A subarray $⟨l, r⟩$ of $A$ is defined as $\[A\_l , A\_{l+1}, \cdots , A\_r]$, and its size is $r - l + 1$.

A value $x$ is the only mode of a subarray $⟨l, r⟩$ if and only if $x$ appears strictly more often than other values in subarray $⟨l, r⟩$.

Your task in this problem is to find, for each $x ∈ \\{0, 1, 2, 3\\}$, the size of the longest subarray of $A$ such that $x$ is the only mode of that subarray, or determine if $x$ cannot be the only mode in any subarray.

Input begins with an integer $N$ ($1 ≤ N ≤ 100\\, 000$) representing the size of array $A$. The next line contains $N$ integers $A\_i$ ($A\_i ∈ \\{0, 1, 2, 3\\}$).

Output four space-separated integers in a single line. Each integer represents the answer where $x$ is $0$, $1$, $2$, and $3$, respectively. For each value of $x$, if there exists a subarray such that $x$ is the only mode in that subarray, then output the size of the longest subarray; otherwise, output $0$.