Dice Throw

You have to perform a sequence of n dice throws. After the nth dice throw there must be at most $A$ times $1$ occurring in the sequence , at most $B$ times $2$ , at most $C$ times $3$ , at most $D$ times $4$ , at most $E$ times $5$ and at most $F$ times $6$ occurring in the whole array of outcomes. Find the number of distinct sequences of dice throws of length $N$ which can occur through rule