You are given inputs N and pairs where N is an integer and pairs is a list of pairs that cannot be in the same subset.\n\nYou are asked to count the number of unique/sorted subsets created from the range 1 to N (inclusive) that do not contain any of the pairs found in the list "pairs". \n\nFor example:\n\n```\nInput : ( 4, [(1, 3), (2, 4)] )\nOutput : 7\n\nExplanation:\nN = 4 so all the possible subsets are \n[(1), (2), (3), (4), (1,2), (2,3), (3,4), (1,2,3), (2,3,4), (1,2,3,4)].\n\nSince Pairs = [(1, 3), (2, 4)], any subsets containing 1 and 3 or 2 and 4 cannot be counted. \nTherefore, the final valid subsets are\n[(1), (2), (3), (4), (1,2), (2,3), (3,4)]\n\n ```\n \n I attempted a brief brute force solution by constructing the power set of the range 1 to N + 1 ```([(1), (2), (3), (4), (1,2), (2,3), (3,4), (1,2,3), (2,3,4), (1,2,3,4)])``` and then going through each pair in pairs and checking to see if all its elements were in the power set.\n \n However, this solution is too slow and I wasn\'t sure on what method I could use to solve this in a faster time. Would really appreciate if someone had a solution or similar problem they could point me to.

You are given inputs N and pairs where N is an integer and pairs is a list of pairs that cannot be in the same subset.\n\nYou are asked to count the number of u