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well they are two different types of drug and per Drugs.com there are 1023 drugs known to interact with the Butrans patch. And yes, the same website lists a major interaction between those two drugs as linked below.Drug Interaction Report - Drugs.com

OMG, imagine if we had a free market in health care, what would happen to prices!!Doctors: No longer would there be a government-imposed shortage of doctors. Medical schools would proliferate. Some specializing in narrow fields for more technical specialities. Some AMA-approved, but other certifications available. Many training programs would not even require a BA prior to medical training. A lot would focus on in-the-field training — helping others and learning as you work.Foreign doctors would come here. Army medics would open small clinics. Gone would be the days when only a tiny fraction of children who wanted to be doctors could be health providers. We’d have a gigantic increase in the number of doctors, nurses, technical assistants. And a resultant dramatic drop in the cost per doctor.And so many things that the government says today that only a doctor can do, would be done by other, lower priced alternatives.Hospitals: No longer would there be a government-imposed shortage of hospitals. There’d be all different types of treatment facilities depending on what they wanted to treat. [1][1][1][1]And if one hospital charged $2,000 a night[2][2][2][2] for a semi-private room, well, another hospital could open right next door and charge only $300 for a bed. And, prices would plummet.Surgeries: The price of surgeries would drop as well. If one hospital charged $40,000 for a procedure, then a hospital that charged $5,000 would get more business[3][3][3][3].[4][4][4][4]Hospital Supplies: And the hospital that charged you $15 for one tylenol, would lose business to the hospital that charged 50¢.[5][5][5][5]New Medicine: And all that added charge for FDA approval? That’d be gone. There’d be a wide range of certifications at varying levels of testing and you and your doctor and insurance carrier would made the tradeoffs with price. New medicines for low incidence diseases would all of a sudden be worth putting out, and it would no longer cost $75,000 for one treatment cycle of chemotherapy[6][6][6][6], because if it did, someone else would offer it at $50,000, and then at $40,000 and so on.Patents: And all the government-enforced monopolies on medicine would disappear overnight. No longer would you be charged $120,000 for a course of medicine whose chemicals cost around $40.Medical Insurance: And the inflated prices of insurance, where the government laws and regulations force you to buy coverage you don’t need at higher prices, would drop significantly. Gone would be the wrapping of health insurance with employment for the purposes of taxes.New companies would rush in to insure different classes of people, and no longer would competitors of the politicians’ cronies being regulated out of business.You see, the ridiculous prices we see today — that have no bearing whatsoever to costs — can only exist in a government-regulated market. Only through the violent threats of government can such disparities continue[7][7][7][7] [8][8][8][8] .Because, if you were any type of entrepreneur and saw somebody regularly selling something that costs 20¢ at a price of $10, you would know that you could make money by undercutting that price. And there are a sufficient number of people who like to make money.But, if the guys overcharging have the bully of government protecting them, not allowing you to undercut them, under penalty of law, they can continue overcharging you and no one can say Boo!The really impressive feat of the government-controlled marketplace is to convince you that the inflated prices you see, which are due entirely to government hinderance of the free market, is actually a function of the free market itself, and that only more government could ever reduce prices.Government cannot reduce price. The way laws and regulations are written inevitably favor some companies and disfavor others. Politicians are too wedded to their cronies, who keep them in power. To pay back their crony, the amount of money taken from you and then given to the crony must rise.The biggest scam they will do, though, is to hide the ever-increasing prices from you. They’ll hide it by paying it through taxes — which are taken from you. And even the “taxes on the corporations” are taken from you via higher prices on products, lower quality products, fewer jobs, lower wages, etc. And the politicians will borrow money to pay their cronies, so your kids will get the bill. And they’ll inflate your money to pay, so that the value of your money disappears even as it sits in your wallet. And the inevitable government-induced shortages will be handled by waits and you’ll move up because others will die.But they’ll have their government teachers “teach” your children in their government schools that their government healthcare is free and abundant and customer oriented and innovative and of the highest quality. And how lucky you are to have your rulers looking out for your health needs.Not like that free market health care, which only cares about making money!See Related0994: How would libertarians reform the FDA?0362: Does the free-market ever work in healthcare?0464: How would healthcare work in a libertarian society?0395: Would a libertarian society have an American Medical Association?1023: Logically speaking, how is healthcare not a right?0485: How might we fairly judge whether the free market or government provides better health care?0566: Should we be allowed to sell our organs?0910: Why is the free market like a religion for Libertarians?0599: In what situations does a free market fail?1107: Can a computer theoretically do better than the market at allocating scarce resources?1046: What's the difference between free market and capitalism?0617: Do libertarians oppose breaking up monopolies if they arise through voluntary interaction?0686: Are the free market and democracy compatible?0397: If universal healthcare providers refuse to work at the fixed wage, is forced labor ethical?0617: Do libertarians oppose breaking up monopolies if they arise through voluntary interaction?→ More essays on <Healthcare> by Dennis→ Return to the <Table of Contents> for Dennis’ Libertarian Essays<, Health, Free Market, Regulation,>Footnotes[1] Medical Price Honesty Benefits Patients at Surgery Center of Oklahoma[1] Medical Price Honesty Benefits Patients at Surgery Center of Oklahoma[1] Medical Price Honesty Benefits Patients at Surgery Center of Oklahoma[1] Medical Price Honesty Benefits Patients at Surgery Center of Oklahoma[2] Average cost per inpatient day across 50 states[2] Average cost per inpatient day across 50 states[2] Average cost per inpatient day across 50 states[2] Average cost per inpatient day across 50 states[3] Surgery Center of Oklahoma[3] Surgery Center of Oklahoma[3] Surgery Center of Oklahoma[3] Surgery Center of Oklahoma[4] What Happens When Doctors Only Take Cash[4] What Happens When Doctors Only Take Cash[4] What Happens When Doctors Only Take Cash[4] What Happens When Doctors Only Take Cash[5] 10 Wildly Overinflated Hospital Costs | Reader's Digest[5] 10 Wildly Overinflated Hospital Costs | Reader's Digest[5] 10 Wildly Overinflated Hospital Costs | Reader's Digest[5] 10 Wildly Overinflated Hospital Costs | Reader's Digest[6] Death by Regulation: The Price We Pay for the FDA[6] Death by Regulation: The Price We Pay for the FDA[6] Death by Regulation: The Price We Pay for the FDA[6] Death by Regulation: The Price We Pay for the FDA[7] How Government Regulations Made Healthcare So Expensive | Mike Holly[7] How Government Regulations Made Healthcare So Expensive | Mike Holly[7] How Government Regulations Made Healthcare So Expensive | Mike Holly[7] How Government Regulations Made Healthcare So Expensive | Mike Holly[8] To Lower Health Care Costs, Try Freedom | Julian Adorney[8] To Lower Health Care Costs, Try Freedom | Julian Adorney[8] To Lower Health Care Costs, Try Freedom | Julian Adorney[8] To Lower Health Care Costs, Try Freedom | Julian Adorney

The question is to summarise a sequence of bitwise operations (|,&,^) to five or fewer such operations. The summarised sequence should give the same result on applying to any integer as the original sequence does.First, note that bitwise operations do not result in any interaction between different positions, so we can just look at what happens to the bits in each position. And there are just four possibilities:0 → 0, 1 → 1. Equivalent to any of |0, &1, ^00 → 0, 1 → 0. Equivalent to &00 → 1, 1 → 0. Equivalent to ^10 → 1, 1 → 1. Equivalent to |1Thus, by following what happens at each bit position, we can decide to apply one each of &, | and ^ operations with the correct arguments and get any desired result. In fact, we need only 2 instead of 3 because &0 is equivalent to |1 followed by ^1. Combining the functions for all positions gives us the answer.The entire process can be performed efficiently with bitwise operationsint N; std::cin >> N; int zeros = 0, ones = 1023; for (int i = 0; i < N; ++i) {  string op;  int x;  std::cin >> op >> x;  if (op == "|") zeros |= x, ones |= x;  else if (op == "&") zeros &= x, ones &= x;  else zeros ^= x, ones ^= x; }  // Map from results for 0 and 1 to or and xor int or_bit[4] = {1, 0, 0, 1}, xor_bit[4] = {1, 0, 1, 0}; int or_val = 0, xor_val = 0; for (int i = 0; i < 10; ++i, zeros >>= 1, ones >>= 1) {  int cur = ((zeros & 1) << 1) | (ones & 1);  or_val |= (or_bit[cur] << i);  xor_val |= (xor_bit[cur] << i); }  std::cout << 2 << "\n"; std::cout << "| " << or_val << "\n"; std::cout << "^ " << xor_val << "\n";