BINARY XOR DECEMBER CHALLENGE 2019

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IF THE LENGTH OF STRING IS 6 HERE N=6

15772493559998329348651081717859|666x500

Can we also solve this problem by dynamic programming if constraints are small.
Here 111100 contains all possible strings having 4 one and 2 zeros and it’s corresponding string on top let’s say having 3 one and 3 zeros then from DP table answer is directly 32.