I am carrot +_+

Probability Level 4

We have a magical carrot multiplier machine, which multiplies an input carrot into at most 6 carrots, and minimum just 1 (gives the carrot back). But it can multiply only original carrots, the ones which were not put into the machine ever.

There are 286286 carrots of 143143 different shades such that there are exactly 22 carrots of each shade. All of these carrots after treating with the machine, are filled in a bag.

There are 11n11^n different compositions possible for this bag. Find nn.

Details and Assumptions:-

\bullet The carrots formed by multiplying one particular carrot are identical (due to magic of the multiplier).

\bullet The 143143 different shades are well distinguishable, no 2 look alike.

This problem is a part of the set Vegetable Combinatorics


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