How many strings of length $3$ formed from the digits $0,1,2$ are there such that for each $j\in 1,2$, at least $j$ of the digits are less than $j$? (For example, $012$ satisfies this condition because it contains at least $1$ digit less than $1$ and at least $2$ digits less than $2$. The string $122$ does not satisfy the condition because it does not contain at least $1$ digit less than $1$.)